X^2-11x+14=2x+2

Solution for X^2-11x+14=2x+2 equation:

X^2-11X+14=2X+2

We move all terms to the left:

X^2-11X+14-(2X+2)=0

We get rid of parentheses

X^2-11X-2X-2+14=0

We add all the numbers together, and all the variables

X^2-13X+12=0

a = 1; b = -13; c = +12;
Δ = b2-4ac
Δ = -132-4·1·12
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-11}{2*1}=\frac{2}{2}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+11}{2*1}=\frac{24}{2}
=12
$