x2-10x+14=3x+2

Solution for x2-10x+14=3x+2 equation:

x2-10x+14=3x+2

We move all terms to the left:

x2-10x+14-(3x+2)=0

We add all the numbers together, and all the variables

x^2-10x-(3x+2)+14=0

We get rid of parentheses

x^2-10x-3x-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
$