-9m+10m(m+3)=-7(m-10)

Solution for -9m+10m(m+3)=-7(m-10) equation:

-9m+10m(m+3)=-7(m-10)

We move all terms to the left:

-9m+10m(m+3)-(-7(m-10))=0

We multiply parentheses

10m^2-9m+30m-(-7(m-10))=0


We calculate terms in parentheses: -(-7(m-10)), so:

-7(m-10)

We multiply parentheses

-7m+70

Back to the equation:

-(-7m+70)


We add all the numbers together, and all the variables

10m^2+21m-(-7m+70)=0

We get rid of parentheses

10m^2+21m+7m-70=0

We add all the numbers together, and all the variables

10m^2+28m-70=0

a = 10; b = 28; c = -70;
Δ = b2-4ac
Δ = 282-4·10·(-70)
Δ = 3584
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:

$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-16\sqrt{14}}{2*10}=\frac{-28-16\sqrt{14}}{20}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+16\sqrt{14}}{2*10}=\frac{-28+16\sqrt{14}}{20}
$