x^2-18x=4x-49

Solution for x^2-18x=4x-49 equation:

x^2-18x=4x-49

We move all terms to the left:

x^2-18x-(4x-49)=0

We get rid of parentheses

x^2-18x-4x+49=0

We add all the numbers together, and all the variables

x^2-22x+49=0

a = 1; b = -22; c = +49;
Δ = b2-4ac
Δ = -222-4·1·49
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-12\sqrt{2}}{2*1}=\frac{22-12\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+12\sqrt{2}}{2*1}=\frac{22+12\sqrt{2}}{2}
$