9x^2+8x=3

Solution for 9x^2+8x=3 equation:

9x^2+8x=3

We move all terms to the left:

9x^2+8x-(3)=0

a = 9; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·9·(-3)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{43}}{2*9}=\frac{-8-2\sqrt{43}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{43}}{2*9}=\frac{-8+2\sqrt{43}}{18}
$