8x^2+5x=2

Solution for 8x^2+5x=2 equation:

8x^2+5x=2

We move all terms to the left:

8x^2+5x-(2)=0

a = 8; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·8·(-2)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{89}}{2*8}=\frac{-5-\sqrt{89}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{89}}{2*8}=\frac{-5+\sqrt{89}}{16}
$