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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(-7+5m(7m+6)+3), so:

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

determiningTheFunctionDomain
5m(7m+6)-7+3

We add all the numbers together, and all the variables

5m(7m+6)-4

We multiply parentheses

35m^2+30m-4

Back to the equation:

-(35m^2+30m-4)


We get rid of parentheses

-35m^2+8m-30m+4-3=0

We add all the numbers together, and all the variables

-35m^2-22m+1=0

a = -35; b = -22; c = +1;
Δ = b2-4ac
Δ = -222-4·(-35)·1
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-4\sqrt{39}}{2*-35}=\frac{22-4\sqrt{39}}{-70}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+4\sqrt{39}}{2*-35}=\frac{22+4\sqrt{39}}{-70}
$