9x^2-45x=-17

Solution for 9x^2-45x=-17 equation:

9x^2-45x=-17

We move all terms to the left:

9x^2-45x-(-17)=0

We add all the numbers together, and all the variables

9x^2-45x+17=0

a = 9; b = -45; c = +17;
Δ = b2-4ac
Δ = -452-4·9·17
Δ = 1413
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:

$\sqrt{\Delta}=\sqrt{1413}=\sqrt{9*157}=\sqrt{9}*\sqrt{157}=3\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{157}}{2*9}=\frac{45-3\sqrt{157}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{157}}{2*9}=\frac{45+3\sqrt{157}}{18}
$