-144x^2+810x-45=0

Solution for -144x^2+810x-45=0 equation:

-144x^2+810x-45=0

a = -144; b = 810; c = -45;
Δ = b2-4ac
Δ = 8102-4·(-144)·(-45)
Δ = 630180
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:

$\sqrt{\Delta}=\sqrt{630180}=\sqrt{324*1945}=\sqrt{324}*\sqrt{1945}=18\sqrt{1945}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(810)-18\sqrt{1945}}{2*-144}=\frac{-810-18\sqrt{1945}}{-288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(810)+18\sqrt{1945}}{2*-144}=\frac{-810+18\sqrt{1945}}{-288}
$