4m^2=14-5m

Solution for 4m^2=14-5m equation:

4m^2=14-5m

We move all terms to the left:

4m^2-(14-5m)=0

We add all the numbers together, and all the variables

4m^2-(-5m+14)=0

We get rid of parentheses

4m^2+5m-14=0

a = 4; b = 5; c = -14;
Δ = b2-4ac
Δ = 52-4·4·(-14)
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*4}=\frac{-5-\sqrt{249}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{249}}{2*4}=\frac{-5+\sqrt{249}}{8}
$