2(x^2)+8(x^2-972)=121.5

Solution for 2(x^2)+8(x^2-972)=121.5 equation:

2(x^2)+8(x^2-972)=121.5

We move all terms to the left:

2(x^2)+8(x^2-972)-(121.5)=0

We add all the numbers together, and all the variables

2x^2+8(x^2-972)-121.5=0

We multiply parentheses

2x^2+8x^2-7776-121.5=0

We add all the numbers together, and all the variables

10x^2-7897.5=0

a = 10; b = 0; c = -7897.5;
Δ = b2-4ac
Δ = 02-4·10·(-7897.5)
Δ = 315900
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:

$\sqrt{\Delta}=\sqrt{315900}=\sqrt{8100*39}=\sqrt{8100}*\sqrt{39}=90\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90\sqrt{39}}{2*10}=\frac{0-90\sqrt{39}}{20}
=-\frac{90\sqrt{39}}{20}
=-\frac{9\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90\sqrt{39}}{2*10}=\frac{0+90\sqrt{39}}{20}
=\frac{90\sqrt{39}}{20}
=\frac{9\sqrt{39}}{2}
$