-9m^2-15m+6=-3-10m^2

Solution for -9m^2-15m+6=-3-10m^2 equation:

-9m^2-15m+6=-3-10m^2

We move all terms to the left:

-9m^2-15m+6-(-3-10m^2)=0

We get rid of parentheses

-9m^2+10m^2-15m+3+6=0

We add all the numbers together, and all the variables

m^2-15m+9=0

a = 1; b = -15; c = +9;
Δ = b2-4ac
Δ = -152-4·1·9
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{21}}{2*1}=\frac{15-3\sqrt{21}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{21}}{2*1}=\frac{15+3\sqrt{21}}{2}
$