10x^2+27x-288=0

Solution for 10x^2+27x-288=0 equation:

10x^2+27x-288=0

a = 10; b = 27; c = -288;
Δ = b2-4ac
Δ = 272-4·10·(-288)
Δ = 12249
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:

$\sqrt{\Delta}=\sqrt{12249}=\sqrt{9*1361}=\sqrt{9}*\sqrt{1361}=3\sqrt{1361}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{1361}}{2*10}=\frac{-27-3\sqrt{1361}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{1361}}{2*10}=\frac{-27+3\sqrt{1361}}{20}
$