5m^2+8m=15

Solution for 5m^2+8m=15 equation:

5m^2+8m=15

We move all terms to the left:

5m^2+8m-(15)=0

a = 5; b = 8; c = -15;
Δ = b2-4ac
Δ = 82-4·5·(-15)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{91}}{2*5}=\frac{-8-2\sqrt{91}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{91}}{2*5}=\frac{-8+2\sqrt{91}}{10}
$