x^2-24x+88=0

Solution for x^2-24x+88=0 equation:

x^2-24x+88=0

a = 1; b = -24; c = +88;
Δ = b2-4ac
Δ = -242-4·1·88
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{14}}{2*1}=\frac{24-4\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{14}}{2*1}=\frac{24+4\sqrt{14}}{2}
$