F.4 MATH quadratic equation!

5x(x-3)+4(x+4)=31-7x^2 ...... (*)
Our target is to convert (*) into the form of ax^2 + bx + c = 0.
5x(x-3)+4(x+4)=31-7x^2
5x^2 - 15x + 4x + 16 = 31 - 7x^2
12x^2 - 11x - 15 = 0
Then solve it by either factorization, completing square or using quadratic formula... or calculator...
Factorization:
12x^2 - 11x - 15 = 0
(3x - 5)(4x + 3) = 0
x = 5/3 or -4/3
Completing Square:
12x^2 - 11x - 15 = 0
12(x^2 - 11x/12) = 15
12[x^2 - 11x / 12 + (11/24)^2 - (11/24)^2] = 15
12(x - 11/24)^2 - 12(121/576) = 15
12(x - 11/24)^2 = 15 + 121 / 48 = 841/48
(x - 11/24)^2 = 841 / 576
x - 11/24 = √(841 / 576) = 29/24
x = (11+29)/24 or (11-29)/24
= 5/3 or -4/3
Quadratic Formula:
12x^2 - 11x - 15 = 0
x = {-(-11)√[(-11)^2 - 4(12)(-15)]} / 2(12)
= (11 √841) / 24
= (11+29)/24 or (11-29)/24
= 5/3 or -4/3

Good Luck for Your Maths Exam!

5x(x-3)+4(x+4)=31-7x^2
5x^2-15x+4x+16=31-7x^2
12x^2-11x-15=0
(4x+3)(3x-5)=0
x=-3/4 or 5/3