4m^2-22m+24=m^2-5m

Solution for 4m^2-22m+24=m^2-5m equation:

4m^2-22m+24=m^2-5m

We move all terms to the left:

4m^2-22m+24-(m^2-5m)=0

We get rid of parentheses

4m^2-m^2-22m+5m+24=0

We add all the numbers together, and all the variables

3m^2-17m+24=0

a = 3; b = -17; c = +24;
Δ = b2-4ac
Δ = -172-4·3·24
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-1}{2*3}=\frac{16}{6}
=2+2/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+1}{2*3}=\frac{18}{6}
=3
$