-x^2+35x=150

Solution for -x^2+35x=150 equation:

-x^2+35x=150

We move all terms to the left:

-x^2+35x-(150)=0

We add all the numbers together, and all the variables

-1x^2+35x-150=0

a = -1; b = 35; c = -150;
Δ = b2-4ac
Δ = 352-4·(-1)·(-150)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-25}{2*-1}=\frac{-60}{-2}
=+30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+25}{2*-1}=\frac{-10}{-2}
=+5
$