how do I solve this problem?

This is how you would solve for x:
start with the problem: -3x^2+343=0
subtract 343 from both sides: -3x^2=-343
then divide -3 from both sides x^2=114.3333 (3 repeating)
then square root both sides and you would get:
app. 10.69
{x|x=10.69}

3x² = 343
x² = 343 / 3
x = ± √ (343/3)
x = ± 10.7 (to 1 dec. place)

3x^2 = 343
x=(sqrt(343/3))

-3x^2+343=0
3x^2=343
x^2=114 1/3
x=10.693 or x= -10.693

-3x^2 + 343 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = -3
b = 0
c = 343

x = [0 ±√(0 + 4116)]/-6
x = [0 ±√4116]/-6
x = [0 ±64.15]/-6 (approx.)

x = 64.15/-6
x = -64.15/6

x = -64.15/-6
x = 64.15/6

∴ x = -64.15/6 , 64.15/6

-3x^2+343=0
-3x^2=-343
3x^2=343
x^2=343/3
x = sqrt(343/3)
x =10.69

Hope this Helps

3x^2=343
x^2=114.33
x=10.69