-75=12x-5x^2

Solution for -75=12x-5x^2 equation:

-75=12x-5x^2

We move all terms to the left:

-75-(12x-5x^2)=0

We get rid of parentheses

5x^2-12x-75=0

a = 5; b = -12; c = -75;
Δ = b2-4ac
Δ = -122-4·5·(-75)
Δ = 1644
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:

$\sqrt{\Delta}=\sqrt{1644}=\sqrt{4*411}=\sqrt{4}*\sqrt{411}=2\sqrt{411}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{411}}{2*5}=\frac{12-2\sqrt{411}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{411}}{2*5}=\frac{12+2\sqrt{411}}{10}
$