-3m(3m-10)-7=-5(m+1)+3m

Solution for -3m(3m-10)-7=-5(m+1)+3m equation:

-3m(3m-10)-7=-5(m+1)+3m

We move all terms to the left:

-3m(3m-10)-7-(-5(m+1)+3m)=0

We multiply parentheses

-9m^2+30m-(-5(m+1)+3m)-7=0


We calculate terms in parentheses: -(-5(m+1)+3m), so:

-5(m+1)+3m

We add all the numbers together, and all the variables

3m-5(m+1)

We multiply parentheses

3m-5m-5

We add all the numbers together, and all the variables

-2m-5

Back to the equation:

-(-2m-5)


We get rid of parentheses

-9m^2+30m+2m+5-7=0

We add all the numbers together, and all the variables

-9m^2+32m-2=0

a = -9; b = 32; c = -2;
Δ = b2-4ac
Δ = 322-4·(-9)·(-2)
Δ = 952
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:

$\sqrt{\Delta}=\sqrt{952}=\sqrt{4*238}=\sqrt{4}*\sqrt{238}=2\sqrt{238}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{238}}{2*-9}=\frac{-32-2\sqrt{238}}{-18}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{238}}{2*-9}=\frac{-32+2\sqrt{238}}{-18}
$