175=4x+x^2

Solution for 175=4x+x^2 equation:

175=4x+x^2

We move all terms to the left:

175-(4x+x^2)=0

We get rid of parentheses

-x^2-4x+175=0

We add all the numbers together, and all the variables

-1x^2-4x+175=0

a = -1; b = -4; c = +175;
Δ = b2-4ac
Δ = -42-4·(-1)·175
Δ = 716
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:

$\sqrt{\Delta}=\sqrt{716}=\sqrt{4*179}=\sqrt{4}*\sqrt{179}=2\sqrt{179}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{179}}{2*-1}=\frac{4-2\sqrt{179}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{179}}{2*-1}=\frac{4+2\sqrt{179}}{-2}
$