X^2-7x+14=5x-6

Solution for X^2-7x+14=5x-6 equation:

X^2-7X+14=5X-6

We move all terms to the left:

X^2-7X+14-(5X-6)=0

We get rid of parentheses

X^2-7X-5X+6+14=0

We add all the numbers together, and all the variables

X^2-12X+20=0

a = 1; b = -12; c = +20;
Δ = b2-4ac
Δ = -122-4·1·20
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8}{2*1}=\frac{4}{2}
=2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8}{2*1}=\frac{20}{2}
=10
$