4x-7=x^2-5x+11

Solution for 4x-7=x^2-5x+11 equation:

4x-7=x^2-5x+11

We move all terms to the left:

4x-7-(x^2-5x+11)=0

We get rid of parentheses

-x^2+4x+5x-11-7=0

We add all the numbers together, and all the variables

-1x^2+9x-18=0

a = -1; b = 9; c = -18;
Δ = b2-4ac
Δ = 92-4·(-1)·(-18)
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{-(9)-3}{2*-1}=\frac{-12}{-2}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*-1}=\frac{-6}{-2}
=+3
$