7m^2=34m-24

Solution for 7m^2=34m-24 equation:

7m^2=34m-24

We move all terms to the left:

7m^2-(34m-24)=0

We get rid of parentheses

7m^2-34m+24=0

a = 7; b = -34; c = +24;
Δ = b2-4ac
Δ = -342-4·7·24
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-22}{2*7}=\frac{12}{14}
=6/7
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+22}{2*7}=\frac{56}{14}
=4
$