4x^2-52x+165=77

Solution for 4x^2-52x+165=77 equation:

4x^2-52x+165=77

We move all terms to the left:

4x^2-52x+165-(77)=0

We add all the numbers together, and all the variables

4x^2-52x+88=0

a = 4; b = -52; c = +88;
Δ = b2-4ac
Δ = -522-4·4·88
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-36}{2*4}=\frac{16}{8}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+36}{2*4}=\frac{88}{8}
=11
$