114750=50(36+x)(60-x)

Solution for 114750=50(36+x)(60-x) equation:

114750=50(36+x)(60-x)

We move all terms to the left:

114750-(50(36+x)(60-x))=0

We add all the numbers together, and all the variables

-(50(x+36)(-1x+60))+114750=0

We multiply parentheses ..

-(50(-1x^2+60x-36x+2160))+114750=0


We calculate terms in parentheses: -(50(-1x^2+60x-36x+2160)), so:

50(-1x^2+60x-36x+2160)

We multiply parentheses

-50x^2+3000x-1800x+108000

We add all the numbers together, and all the variables

-50x^2+1200x+108000

Back to the equation:

-(-50x^2+1200x+108000)


We get rid of parentheses

50x^2-1200x-108000+114750=0

We add all the numbers together, and all the variables

50x^2-1200x+6750=0

a = 50; b = -1200; c = +6750;
Δ = b2-4ac
Δ = -12002-4·50·6750
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-300}{2*50}=\frac{900}{100}
=9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+300}{2*50}=\frac{1500}{100}
=15
$