X^2-4x=3x-8

Solution for X^2-4x=3x-8 equation:

X^2-4X=3X-8

We move all terms to the left:

X^2-4X-(3X-8)=0

We get rid of parentheses

X^2-4X-3X+8=0

We add all the numbers together, and all the variables

X^2-7X+8=0

a = 1; b = -7; c = +8;
Δ = b2-4ac
Δ = -72-4·1·8
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{17}}{2*1}=\frac{7-\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{17}}{2*1}=\frac{7+\sqrt{17}}{2}
$