15x2+22x=8

Solution for 15x2+22x=8 equation:

15x^2+22x=8

We move all terms to the left:

15x^2+22x-(8)=0

a = 15; b = 22; c = -8;
Δ = b2-4ac
Δ = 222-4·15·(-8)
Δ = 964
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:

$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{241}}{2*15}=\frac{-22-2\sqrt{241}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{241}}{2*15}=\frac{-22+2\sqrt{241}}{30}
$