x(8x-5)=50

Solution for x(8x-5)=50 equation:

x(8x-5)=50

We move all terms to the left:

x(8x-5)-(50)=0

We multiply parentheses

8x^2-5x-50=0

a = 8; b = -5; c = -50;
Δ = b2-4ac
Δ = -52-4·8·(-50)
Δ = 1625
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:

$\sqrt{\Delta}=\sqrt{1625}=\sqrt{25*65}=\sqrt{25}*\sqrt{65}=5\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{65}}{2*8}=\frac{5-5\sqrt{65}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{65}}{2*8}=\frac{5+5\sqrt{65}}{16}
$