7m^2-5m-29=0

Solution for 7m^2-5m-29=0 equation:

7m^2-5m-29=0

a = 7; b = -5; c = -29;
Δ = b2-4ac
Δ = -52-4·7·(-29)
Δ = 837
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:

$\sqrt{\Delta}=\sqrt{837}=\sqrt{9*93}=\sqrt{9}*\sqrt{93}=3\sqrt{93}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{93}}{2*7}=\frac{5-3\sqrt{93}}{14}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{93}}{2*7}=\frac{5+3\sqrt{93}}{14}
$