40x^2+24x=24

Solution for 40x^2+24x=24 equation:

40x^2+24x=24

We move all terms to the left:

40x^2+24x-(24)=0

a = 40; b = 24; c = -24;
Δ = b2-4ac
Δ = 242-4·40·(-24)
Δ = 4416
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:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{69}}{2*40}=\frac{-24-8\sqrt{69}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{69}}{2*40}=\frac{-24+8\sqrt{69}}{80}
$