5m-14+3m+8+2m-7+3/2m+2=58

Solution for 5m-14+3m+8+2m-7+3/2m+2=58 equation:

5m-14+3m+8+2m-7+3/2m+2=58

We move all terms to the left:

5m-14+3m+8+2m-7+3/2m+2-(58)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

10m+3/2m-69=0

We multiply all the terms by the denominator


10m*2m-69*2m+3=0

Wy multiply elements

20m^2-138m+3=0

a = 20; b = -138; c = +3;
Δ = b2-4ac
Δ = -1382-4·20·3
Δ = 18804
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:

$\sqrt{\Delta}=\sqrt{18804}=\sqrt{4*4701}=\sqrt{4}*\sqrt{4701}=2\sqrt{4701}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-2\sqrt{4701}}{2*20}=\frac{138-2\sqrt{4701}}{40}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+2\sqrt{4701}}{2*20}=\frac{138+2\sqrt{4701}}{40}
$