X^2-13x+57=2x+3

Solution for X^2-13x+57=2x+3 equation:

X^2-13X+57=2X+3

We move all terms to the left:

X^2-13X+57-(2X+3)=0

We get rid of parentheses

X^2-13X-2X-3+57=0

We add all the numbers together, and all the variables

X^2-15X+54=0

a = 1; b = -15; c = +54;
Δ = b2-4ac
Δ = -152-4·1·54
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3}{2*1}=\frac{12}{2}
=6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3}{2*1}=\frac{18}{2}
=9
$