m^2+7m-15/4=0

Solution for m^2+7m-15/4=0 equation:

m^2+7m-15/4=0

We multiply all the terms by the denominator


m^2*4+7m*4-15=0

Wy multiply elements

4m^2+28m-15=0

a = 4; b = 28; c = -15;
Δ = b2-4ac
Δ = 282-4·4·(-15)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-32}{2*4}=\frac{-60}{8}
=-7+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+32}{2*4}=\frac{4}{8}
=1/2
$