5m+4=7m(m+1)-2m

Solution for 5m+4=7m(m+1)-2m equation:

5m+4=7m(m+1)-2m

We move all terms to the left:

5m+4-(7m(m+1)-2m)=0


We calculate terms in parentheses: -(7m(m+1)-2m), so:

7m(m+1)-2m

We add all the numbers together, and all the variables

-2m+7m(m+1)

We multiply parentheses

7m^2-2m+7m

We add all the numbers together, and all the variables

7m^2+5m

Back to the equation:

-(7m^2+5m)


We get rid of parentheses

-7m^2+5m-5m+4=0

We add all the numbers together, and all the variables

-7m^2+4=0

a = -7; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-7)·4
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*-7}=\frac{0-4\sqrt{7}}{-14}
=-\frac{4\sqrt{7}}{-14}
=-\frac{2\sqrt{7}}{-7}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*-7}=\frac{0+4\sqrt{7}}{-14}
=\frac{4\sqrt{7}}{-14}
=\frac{2\sqrt{7}}{-7}
$