(m+1)(2m-3)=6

Solution for (m+1)(2m-3)=6 equation:

(m+1)(2m-3)=6

We move all terms to the left:

(m+1)(2m-3)-(6)=0

We multiply parentheses ..

(+2m^2-3m+2m-3)-6=0

We get rid of parentheses

2m^2-3m+2m-3-6=0

We add all the numbers together, and all the variables

2m^2-1m-9=0

a = 2; b = -1; c = -9;
Δ = b2-4ac
Δ = -12-4·2·(-9)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{73}}{2*2}=\frac{1-\sqrt{73}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{73}}{2*2}=\frac{1+\sqrt{73}}{4}
$