150x+10000=-2x^2+600x

Solution for 150x+10000=-2x^2+600x equation:

150x+10000=-2x^2+600x

We move all terms to the left:

150x+10000-(-2x^2+600x)=0

We get rid of parentheses

2x^2-600x+150x+10000=0

We add all the numbers together, and all the variables

2x^2-450x+10000=0

a = 2; b = -450; c = +10000;
Δ = b2-4ac
Δ = -4502-4·2·10000
Δ = 122500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{122500}=350$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-350}{2*2}=\frac{100}{4}
=25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+350}{2*2}=\frac{800}{4}
=200
$