x*(x+6)=6075

Solution for x*(x+6)=6075 equation:

x(x+6)=6075

We move all terms to the left:

x(x+6)-(6075)=0

We multiply parentheses

x^2+6x-6075=0

a = 1; b = 6; c = -6075;
Δ = b2-4ac
Δ = 62-4·1·(-6075)
Δ = 24336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24336}=156$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-156}{2*1}=\frac{-162}{2}
=-81
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+156}{2*1}=\frac{150}{2}
=75
$