6x^2+8x=9

Solution for 6x^2+8x=9 equation:

6x^2+8x=9

We move all terms to the left:

6x^2+8x-(9)=0

a = 6; b = 8; c = -9;
Δ = b2-4ac
Δ = 82-4·6·(-9)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{70}}{2*6}=\frac{-8-2\sqrt{70}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{70}}{2*6}=\frac{-8+2\sqrt{70}}{12}
$