-10x^2+105x+30=75

Solution for -10x^2+105x+30=75 equation:

-10x^2+105x+30=75

We move all terms to the left:

-10x^2+105x+30-(75)=0

We add all the numbers together, and all the variables

-10x^2+105x-45=0

a = -10; b = 105; c = -45;
Δ = b2-4ac
Δ = 1052-4·(-10)·(-45)
Δ = 9225
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:

$\sqrt{\Delta}=\sqrt{9225}=\sqrt{225*41}=\sqrt{225}*\sqrt{41}=15\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-15\sqrt{41}}{2*-10}=\frac{-105-15\sqrt{41}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+15\sqrt{41}}{2*-10}=\frac{-105+15\sqrt{41}}{-20}
$