x2-8x+14=3x-4

Solution for x2-8x+14=3x-4 equation:

x2-8x+14=3x-4

We move all terms to the left:

x2-8x+14-(3x-4)=0

We add all the numbers together, and all the variables

x^2-8x-(3x-4)+14=0

We get rid of parentheses

x^2-8x-3x+4+14=0

We add all the numbers together, and all the variables

x^2-11x+18=0

a = 1; b = -11; c = +18;
Δ = b2-4ac
Δ = -112-4·1·18
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-7}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7}{2*1}=\frac{18}{2}
=9
$