4x(x-2)=30

Solution for 4x(x-2)=30 equation:

4x(x-2)=30

We move all terms to the left:

4x(x-2)-(30)=0

We multiply parentheses

4x^2-8x-30=0

a = 4; b = -8; c = -30;
Δ = b2-4ac
Δ = -82-4·4·(-30)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{34}}{2*4}=\frac{8-4\sqrt{34}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{34}}{2*4}=\frac{8+4\sqrt{34}}{8}
$