5x(x-8)=30

Solution for 5x(x-8)=30 equation:

5x(x-8)=30

We move all terms to the left:

5x(x-8)-(30)=0

We multiply parentheses

5x^2-40x-30=0

a = 5; b = -40; c = -30;
Δ = b2-4ac
Δ = -402-4·5·(-30)
Δ = 2200
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:

$\sqrt{\Delta}=\sqrt{2200}=\sqrt{100*22}=\sqrt{100}*\sqrt{22}=10\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{22}}{2*5}=\frac{40-10\sqrt{22}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{22}}{2*5}=\frac{40+10\sqrt{22}}{10}
$