(m-3)(m+8)=7m

Solution for (m-3)(m+8)=7m equation:

(m-3)(m+8)=7m

We move all terms to the left:

(m-3)(m+8)-(7m)=0

We add all the numbers together, and all the variables

-7m+(m-3)(m+8)=0

We multiply parentheses ..

(+m^2+8m-3m-24)-7m=0

We get rid of parentheses

m^2+8m-3m-7m-24=0

We add all the numbers together, and all the variables

m^2-2m-24=0

a = 1; b = -2; c = -24;
Δ = b2-4ac
Δ = -22-4·1·(-24)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*1}=\frac{-8}{2}
=-4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*1}=\frac{12}{2}
=6
$