-5m^2+12m+8=3-5m

Solution for -5m^2+12m+8=3-5m equation:

-5m^2+12m+8=3-5m

We move all terms to the left:

-5m^2+12m+8-(3-5m)=0

We add all the numbers together, and all the variables

-5m^2+12m-(-5m+3)+8=0

We get rid of parentheses

-5m^2+12m+5m-3+8=0

We add all the numbers together, and all the variables

-5m^2+17m+5=0

a = -5; b = 17; c = +5;
Δ = b2-4ac
Δ = 172-4·(-5)·5
Δ = 389
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{389}}{2*-5}=\frac{-17-\sqrt{389}}{-10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{389}}{2*-5}=\frac{-17+\sqrt{389}}{-10}
$