89x^2+4x-24=0

Solution for 89x^2+4x-24=0 equation:

89x^2+4x-24=0

a = 89; b = 4; c = -24;
Δ = b2-4ac
Δ = 42-4·89·(-24)
Δ = 8560
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:

$\sqrt{\Delta}=\sqrt{8560}=\sqrt{16*535}=\sqrt{16}*\sqrt{535}=4\sqrt{535}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{535}}{2*89}=\frac{-4-4\sqrt{535}}{178}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{535}}{2*89}=\frac{-4+4\sqrt{535}}{178}
$