X2-12x+43=3x-1

Solution for X2-12x+43=3x-1 equation:

X2-12X+43=3X-1

We move all terms to the left:

X2-12X+43-(3X-1)=0

We add all the numbers together, and all the variables

X^2-12X-(3X-1)+43=0

We get rid of parentheses

X^2-12X-3X+1+43=0

We add all the numbers together, and all the variables

X^2-15X+44=0

a = 1; b = -15; c = +44;
Δ = b2-4ac
Δ = -152-4·1·44
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{-(-15)-7}{2*1}=\frac{8}{2}
=4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+7}{2*1}=\frac{22}{2}
=11
$