8(x^2-10)=40

Solution for 8(x^2-10)=40 equation:

8(x^2-10)=40

We move all terms to the left:

8(x^2-10)-(40)=0

We multiply parentheses

8x^2-80-40=0

We add all the numbers together, and all the variables

8x^2-120=0

a = 8; b = 0; c = -120;
Δ = b2-4ac
Δ = 02-4·8·(-120)
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{15}}{2*8}=\frac{0-16\sqrt{15}}{16}
=-\frac{16\sqrt{15}}{16}
=-\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{15}}{2*8}=\frac{0+16\sqrt{15}}{16}
=\frac{16\sqrt{15}}{16}
=\sqrt{15}
$