188-6x^2=32

Solution for 188-6x^2=32 equation:

188-6x^2=32

We move all terms to the left:

188-6x^2-(32)=0

We add all the numbers together, and all the variables

-6x^2+156=0

a = -6; b = 0; c = +156;
Δ = b2-4ac
Δ = 02-4·(-6)·156
Δ = 3744
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:

$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{26}}{2*-6}=\frac{0-12\sqrt{26}}{-12}
=-\frac{12\sqrt{26}}{-12}
=-\frac{\sqrt{26}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{26}}{2*-6}=\frac{0+12\sqrt{26}}{-12}
=\frac{12\sqrt{26}}{-12}
=\frac{\sqrt{26}}{-1}
$