8x^2=9x+2

Solution for 8x^2=9x+2 equation:

8x^2=9x+2

We move all terms to the left:

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

We get rid of parentheses

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}
$