8m-3=-7+5m(6+7m)

Solution for 8m-3=-7+5m(6+7m) equation:

8m-3=-7+5m(6+7m)

We move all terms to the left:

8m-3-(-7+5m(6+7m))=0

We add all the numbers together, and all the variables

8m-(-7+5m(7m+6))-3=0


We calculate terms in parentheses: -(-7+5m(7m+6)), so:

-7+5m(7m+6)

determiningTheFunctionDomain
5m(7m+6)-7

We multiply parentheses

35m^2+30m-7

Back to the equation:

-(35m^2+30m-7)


We get rid of parentheses

-35m^2+8m-30m+7-3=0

We add all the numbers together, and all the variables

-35m^2-22m+4=0

a = -35; b = -22; c = +4;
Δ = b2-4ac
Δ = -222-4·(-35)·4
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-6\sqrt{29}}{2*-35}=\frac{22-6\sqrt{29}}{-70}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+6\sqrt{29}}{2*-35}=\frac{22+6\sqrt{29}}{-70}
$