8x(2x-10)=52

Solution for 8x(2x-10)=52 equation:

8x(2x-10)=52

We move all terms to the left:

8x(2x-10)-(52)=0

We multiply parentheses

16x^2-80x-52=0

a = 16; b = -80; c = -52;
Δ = b2-4ac
Δ = -802-4·16·(-52)
Δ = 9728
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:

$\sqrt{\Delta}=\sqrt{9728}=\sqrt{256*38}=\sqrt{256}*\sqrt{38}=16\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-16\sqrt{38}}{2*16}=\frac{80-16\sqrt{38}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+16\sqrt{38}}{2*16}=\frac{80+16\sqrt{38}}{32}
$