X^2-4x+23=7x+5

Solution for X^2-4x+23=7x+5 equation:

X^2-4X+23=7X+5

We move all terms to the left:

X^2-4X+23-(7X+5)=0

We get rid of parentheses

X^2-4X-7X-5+23=0

We add all the numbers together, and all the variables

X^2-11X+18=0

a = 1; b = -11; c = +18;
Δ = b2-4ac
Δ = -112-4·1·18
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{-(-11)-7}{2*1}=\frac{4}{2}
=2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7}{2*1}=\frac{18}{2}
=9
$