121x^2-110x=9

Solution for 121x^2-110x=9 equation:

121x^2-110x=9

We move all terms to the left:

121x^2-110x-(9)=0

a = 121; b = -110; c = -9;
Δ = b2-4ac
Δ = -1102-4·121·(-9)
Δ = 16456
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:

$\sqrt{\Delta}=\sqrt{16456}=\sqrt{484*34}=\sqrt{484}*\sqrt{34}=22\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-22\sqrt{34}}{2*121}=\frac{110-22\sqrt{34}}{242}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+22\sqrt{34}}{2*121}=\frac{110+22\sqrt{34}}{242}
$