9x2-8x+9=15

Solution for 9x2-8x+9=15 equation:

9x^2-8x+9=15

We move all terms to the left:

9x^2-8x+9-(15)=0

We add all the numbers together, and all the variables

9x^2-8x-6=0

a = 9; b = -8; c = -6;
Δ = b2-4ac
Δ = -82-4·9·(-6)
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*9}=\frac{8-2\sqrt{70}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{70}}{2*9}=\frac{8+2\sqrt{70}}{18}
$