(120+2x)(70+2x)-15000=0

Solution for (120+2x)(70+2x)-15000=0 equation:

(120+2x)(70+2x)-15000=0

We add all the numbers together, and all the variables

(2x+120)(2x+70)-15000=0

We multiply parentheses ..

(+4x^2+140x+240x+8400)-15000=0

We get rid of parentheses

4x^2+140x+240x+8400-15000=0

We add all the numbers together, and all the variables

4x^2+380x-6600=0

a = 4; b = 380; c = -6600;
Δ = b2-4ac
Δ = 3802-4·4·(-6600)
Δ = 250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{250000}=500$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(380)-500}{2*4}=\frac{-880}{8}
=-110
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(380)+500}{2*4}=\frac{120}{8}
=15
$