375=(50+2x)(30+2x)-1500

Solution for 375=(50+2x)(30+2x)-1500 equation:

375=(50+2x)(30+2x)-1500

We move all terms to the left:

375-((50+2x)(30+2x)-1500)=0

We add all the numbers together, and all the variables

-((2x+50)(2x+30)-1500)+375=0

We multiply parentheses ..

-((+4x^2+60x+100x+1500)-1500)+375=0


We calculate terms in parentheses: -((+4x^2+60x+100x+1500)-1500), so:

(+4x^2+60x+100x+1500)-1500

We get rid of parentheses

4x^2+60x+100x+1500-1500

We add all the numbers together, and all the variables

4x^2+160x

Back to the equation:

-(4x^2+160x)


We get rid of parentheses

-4x^2-160x+375=0

a = -4; b = -160; c = +375;
Δ = b2-4ac
Δ = -1602-4·(-4)·375
Δ = 31600
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:

$\sqrt{\Delta}=\sqrt{31600}=\sqrt{400*79}=\sqrt{400}*\sqrt{79}=20\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-20\sqrt{79}}{2*-4}=\frac{160-20\sqrt{79}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+20\sqrt{79}}{2*-4}=\frac{160+20\sqrt{79}}{-8}
$