8m^2-7=-5m

Solution for 8m^2-7=-5m equation:

8m^2-7=-5m

We move all terms to the left:

8m^2-7-(-5m)=0

We get rid of parentheses

8m^2+5m-7=0

a = 8; b = 5; c = -7;
Δ = b2-4ac
Δ = 52-4·8·(-7)
Δ = 249
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{-(5)-\sqrt{249}}{2*8}=\frac{-5-\sqrt{249}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{249}}{2*8}=\frac{-5+\sqrt{249}}{16}
$