4x^2-6x+9=121

Solution for 4x^2-6x+9=121 equation:

4x^2-6x+9=121

We move all terms to the left:

4x^2-6x+9-(121)=0

We add all the numbers together, and all the variables

4x^2-6x-112=0

a = 4; b = -6; c = -112;
Δ = b2-4ac
Δ = -62-4·4·(-112)
Δ = 1828
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:

$\sqrt{\Delta}=\sqrt{1828}=\sqrt{4*457}=\sqrt{4}*\sqrt{457}=2\sqrt{457}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{457}}{2*4}=\frac{6-2\sqrt{457}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{457}}{2*4}=\frac{6+2\sqrt{457}}{8}
$