100x-100x+1500-6x^2+90=0

Solution for 100x-100x+1500-6x^2+90=0 equation:

100x-100x+1500-6x^2+90=0

We add all the numbers together, and all the variables

-6x^2+1590=0

a = -6; b = 0; c = +1590;
Δ = b2-4ac
Δ = 02-4·(-6)·1590
Δ = 38160
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:

$\sqrt{\Delta}=\sqrt{38160}=\sqrt{144*265}=\sqrt{144}*\sqrt{265}=12\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{265}}{2*-6}=\frac{0-12\sqrt{265}}{-12}
=-\frac{12\sqrt{265}}{-12}
=-\frac{\sqrt{265}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{265}}{2*-6}=\frac{0+12\sqrt{265}}{-12}
=\frac{12\sqrt{265}}{-12}
=\frac{\sqrt{265}}{-1}
$