2x+75=x^2

Solution for 2x+75=x^2 equation:

2x+75=x^2

We move all terms to the left:

2x+75-(x^2)=0

determiningTheFunctionDomain
-x^2+2x+75=0

We add all the numbers together, and all the variables

-1x^2+2x+75=0

a = -1; b = 2; c = +75;
Δ = b2-4ac
Δ = 22-4·(-1)·75
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{19}}{2*-1}=\frac{-2-4\sqrt{19}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{19}}{2*-1}=\frac{-2+4\sqrt{19}}{-2}
$