(4x-100)(x+5)=30

Solution for (4x-100)(x+5)=30 equation:

(4x-100)(x+5)=30

We move all terms to the left:

(4x-100)(x+5)-(30)=0

We multiply parentheses ..

(+4x^2+20x-100x-500)-30=0

We get rid of parentheses

4x^2+20x-100x-500-30=0

We add all the numbers together, and all the variables

4x^2-80x-530=0

a = 4; b = -80; c = -530;
Δ = b2-4ac
Δ = -802-4·4·(-530)
Δ = 14880
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:

$\sqrt{\Delta}=\sqrt{14880}=\sqrt{16*930}=\sqrt{16}*\sqrt{930}=4\sqrt{930}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{930}}{2*4}=\frac{80-4\sqrt{930}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{930}}{2*4}=\frac{80+4\sqrt{930}}{8}
$