x^2=48+22x

Solution for x^2=48+22x equation:

x^2=48+22x

We move all terms to the left:

x^2-(48+22x)=0

We add all the numbers together, and all the variables

x^2-(22x+48)=0

We get rid of parentheses

x^2-22x-48=0

a = 1; b = -22; c = -48;
Δ = b2-4ac
Δ = -222-4·1·(-48)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-26}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+26}{2*1}=\frac{48}{2}
=24
$