-4(2m+5)-(3)/(4)m=22

Solution for -4(2m+5)-(3)/(4)m=22 equation:

-4(2m+5)-(3)/(4)m=22

We move all terms to the left:

-4(2m+5)-(3)/(4)m-(22)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We multiply parentheses

-8m-3/4m-20-22=0

We multiply all the terms by the denominator


-8m*4m-20*4m-22*4m-3=0

Wy multiply elements

-32m^2-80m-88m-3=0

We add all the numbers together, and all the variables

-32m^2-168m-3=0

a = -32; b = -168; c = -3;
Δ = b2-4ac
Δ = -1682-4·(-32)·(-3)
Δ = 27840
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:

$\sqrt{\Delta}=\sqrt{27840}=\sqrt{64*435}=\sqrt{64}*\sqrt{435}=8\sqrt{435}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-8\sqrt{435}}{2*-32}=\frac{168-8\sqrt{435}}{-64}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+8\sqrt{435}}{2*-32}=\frac{168+8\sqrt{435}}{-64}
$