10x2+24x=8

Solution for 10x2+24x=8 equation:

10x^2+24x=8

We move all terms to the left:

10x^2+24x-(8)=0

a = 10; b = 24; c = -8;
Δ = b2-4ac
Δ = 242-4·10·(-8)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{14}}{2*10}=\frac{-24-8\sqrt{14}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{14}}{2*10}=\frac{-24+8\sqrt{14}}{20}
$