5x^2-45x-288=0

Solution for 5x^2-45x-288=0 equation:

5x^2-45x-288=0

a = 5; b = -45; c = -288;
Δ = b2-4ac
Δ = -452-4·5·(-288)
Δ = 7785
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:

$\sqrt{\Delta}=\sqrt{7785}=\sqrt{9*865}=\sqrt{9}*\sqrt{865}=3\sqrt{865}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{865}}{2*5}=\frac{45-3\sqrt{865}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{865}}{2*5}=\frac{45+3\sqrt{865}}{10}
$