13x^2-24x=288

Solution for 13x^2-24x=288 equation:

13x^2-24x=288

We move all terms to the left:

13x^2-24x-(288)=0

a = 13; b = -24; c = -288;
Δ = b2-4ac
Δ = -242-4·13·(-288)
Δ = 15552
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:

$\sqrt{\Delta}=\sqrt{15552}=\sqrt{5184*3}=\sqrt{5184}*\sqrt{3}=72\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-72\sqrt{3}}{2*13}=\frac{24-72\sqrt{3}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+72\sqrt{3}}{2*13}=\frac{24+72\sqrt{3}}{26}
$