180x+16000=2x^2+660x

Solution for 180x+16000=2x^2+660x equation:

180x+16000=2x^2+660x

We move all terms to the left:

180x+16000-(2x^2+660x)=0

We get rid of parentheses

-2x^2+180x-660x+16000=0

We add all the numbers together, and all the variables

-2x^2-480x+16000=0

a = -2; b = -480; c = +16000;
Δ = b2-4ac
Δ = -4802-4·(-2)·16000
Δ = 358400
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:

$\sqrt{\Delta}=\sqrt{358400}=\sqrt{25600*14}=\sqrt{25600}*\sqrt{14}=160\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-160\sqrt{14}}{2*-2}=\frac{480-160\sqrt{14}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+160\sqrt{14}}{2*-2}=\frac{480+160\sqrt{14}}{-4}
$