7m^2+6m-5=0

Solution for 7m^2+6m-5=0 equation:

7m^2+6m-5=0

a = 7; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·7·(-5)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{11}}{2*7}=\frac{-6-4\sqrt{11}}{14}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{11}}{2*7}=\frac{-6+4\sqrt{11}}{14}
$