x^2+(x^2-28x+196)=1156

Solution for x^2+(x^2-28x+196)=1156 equation:

x^2+(x^2-28x+196)=1156

We move all terms to the left:

x^2+(x^2-28x+196)-(1156)=0

We get rid of parentheses

x^2+x^2-28x+196-1156=0

We add all the numbers together, and all the variables

2x^2-28x-960=0

a = 2; b = -28; c = -960;
Δ = b2-4ac
Δ = -282-4·2·(-960)
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-92}{2*2}=\frac{-64}{4}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+92}{2*2}=\frac{120}{4}
=30
$