400=6x^2-152

Solution for 400=6x^2-152 equation:

400=6x^2-152

We move all terms to the left:

400-(6x^2-152)=0

We get rid of parentheses

-6x^2+152+400=0

We add all the numbers together, and all the variables

-6x^2+552=0

a = -6; b = 0; c = +552;
Δ = b2-4ac
Δ = 02-4·(-6)·552
Δ = 13248
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{13248}=\sqrt{576*23}=\sqrt{576}*\sqrt{23}=24\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{23}}{2*-6}=\frac{0-24\sqrt{23}}{-12}
=-\frac{24\sqrt{23}}{-12}
=-\frac{2\sqrt{23}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{23}}{2*-6}=\frac{0+24\sqrt{23}}{-12}
=\frac{24\sqrt{23}}{-12}
=\frac{2\sqrt{23}}{-1}
$