900x-10x^2=20

Solution for 900x-10x^2=20 equation:

900x-10x^2=20

We move all terms to the left:

900x-10x^2-(20)=0

a = -10; b = 900; c = -20;
Δ = b2-4ac
Δ = 9002-4·(-10)·(-20)
Δ = 809200
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:

$\sqrt{\Delta}=\sqrt{809200}=\sqrt{115600*7}=\sqrt{115600}*\sqrt{7}=340\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(900)-340\sqrt{7}}{2*-10}=\frac{-900-340\sqrt{7}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(900)+340\sqrt{7}}{2*-10}=\frac{-900+340\sqrt{7}}{-20}
$