8x2+9x=2

Solution for 8x2+9x=2 equation:

8x^2+9x=2

We move all terms to the left:

8x^2+9x-(2)=0

a = 8; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·8·(-2)
Δ = 145
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{-(9)-\sqrt{145}}{2*8}=\frac{-9-\sqrt{145}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{145}}{2*8}=\frac{-9+\sqrt{145}}{16}
$