7500=4c(c+50)

Solution for 7500=4c(c+50) equation:

7500=4c(c+50)

We move all terms to the left:

7500-(4c(c+50))=0


We calculate terms in parentheses: -(4c(c+50)), so:

4c(c+50)

We multiply parentheses

4c^2+200c

Back to the equation:

-(4c^2+200c)


We get rid of parentheses

-4c^2-200c+7500=0

a = -4; b = -200; c = +7500;
Δ = b2-4ac
Δ = -2002-4·(-4)·7500
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-400}{2*-4}=\frac{-200}{-8}
=+25
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+400}{2*-4}=\frac{600}{-8}
=-75
$