4m^2+5m=3

Solution for 4m^2+5m=3 equation:

4m^2+5m=3

We move all terms to the left:

4m^2+5m-(3)=0

a = 4; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·4·(-3)
Δ = 73
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{73}}{2*4}=\frac{-5-\sqrt{73}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*4}=\frac{-5+\sqrt{73}}{8}
$