9x^2-30x+16=9

Solution for 9x^2-30x+16=9 equation:

9x^2-30x+16=9

We move all terms to the left:

9x^2-30x+16-(9)=0

We add all the numbers together, and all the variables

9x^2-30x+7=0

a = 9; b = -30; c = +7;
Δ = b2-4ac
Δ = -302-4·9·7
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-18\sqrt{2}}{2*9}=\frac{30-18\sqrt{2}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+18\sqrt{2}}{2*9}=\frac{30+18\sqrt{2}}{18}
$