176x=121+x^2

Solution for 176x=121+x^2 equation:

176x=121+x^2

We move all terms to the left:

176x-(121+x^2)=0

We get rid of parentheses

-x^2+176x-121=0

We add all the numbers together, and all the variables

-1x^2+176x-121=0

a = -1; b = 176; c = -121;
Δ = b2-4ac
Δ = 1762-4·(-1)·(-121)
Δ = 30492
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:

$\sqrt{\Delta}=\sqrt{30492}=\sqrt{4356*7}=\sqrt{4356}*\sqrt{7}=66\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(176)-66\sqrt{7}}{2*-1}=\frac{-176-66\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(176)+66\sqrt{7}}{2*-1}=\frac{-176+66\sqrt{7}}{-2}
$