7/8m+5-2-9m=52

Solution for 7/8m+5-2-9m=52 equation:

7/8m+5-2-9m=52

We move all terms to the left:

7/8m+5-2-9m-(52)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R


We add all the numbers together, and all the variables

-9m+7/8m-49=0

We multiply all the terms by the denominator


-9m*8m-49*8m+7=0

Wy multiply elements

-72m^2-392m+7=0

a = -72; b = -392; c = +7;
Δ = b2-4ac
Δ = -3922-4·(-72)·7
Δ = 155680
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:

$\sqrt{\Delta}=\sqrt{155680}=\sqrt{16*9730}=\sqrt{16}*\sqrt{9730}=4\sqrt{9730}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-392)-4\sqrt{9730}}{2*-72}=\frac{392-4\sqrt{9730}}{-144}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-392)+4\sqrt{9730}}{2*-72}=\frac{392+4\sqrt{9730}}{-144}
$