4m^2-21m+10=-5m^2

Solution for 4m^2-21m+10=-5m^2 equation:

4m^2-21m+10=-5m^2

We move all terms to the left:

4m^2-21m+10-(-5m^2)=0

We get rid of parentheses

4m^2+5m^2-21m+10=0

We add all the numbers together, and all the variables

9m^2-21m+10=0

a = 9; b = -21; c = +10;
Δ = b2-4ac
Δ = -212-4·9·10
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-9}{2*9}=\frac{12}{18}
=2/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+9}{2*9}=\frac{30}{18}
=1+2/3
$