-2x2+30x=100

Solution for -2x2+30x=100 equation:

-2x^2+30x=100

We move all terms to the left:

-2x^2+30x-(100)=0

a = -2; b = 30; c = -100;
Δ = b2-4ac
Δ = 302-4·(-2)·(-100)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10}{2*-2}=\frac{-40}{-4}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10}{2*-2}=\frac{-20}{-4}
=+5
$