(0.75x)(50+x)=15000

Solution for (0.75x)(50+x)=15000 equation:

(0.75x)(50+x)=15000

We move all terms to the left:

(0.75x)(50+x)-(15000)=0

We add all the numbers together, and all the variables

(+0.75x)(x+50)-15000=0

We multiply parentheses ..

(+0x^2+0x)-15000=0

We get rid of parentheses

0x^2+0x-15000=0

We add all the numbers together, and all the variables

x^2+x-15000=0

a = 1; b = 1; c = -15000;
Δ = b2-4ac
Δ = 12-4·1·(-15000)
Δ = 60001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{60001}}{2*1}=\frac{-1-\sqrt{60001}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{60001}}{2*1}=\frac{-1+\sqrt{60001}}{2}
$