4/5*m=28

Solution for 4/5*m=28 equation:

4/5*m=28

We move all terms to the left:

4/5*m-(28)=0


Domain of the equation: 5*m!=0

m!=0/1

m!=0

m∈R


We multiply all the terms by the denominator


-28*5*m+4=0

Wy multiply elements

-140m*m+4=0

Wy multiply elements

-140m^2+4=0

a = -140; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-140)·4
Δ = 2240
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:

$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{35}}{2*-140}=\frac{0-8\sqrt{35}}{-280}
=-\frac{8\sqrt{35}}{-280}
=-\frac{\sqrt{35}}{-35}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{35}}{2*-140}=\frac{0+8\sqrt{35}}{-280}
=\frac{8\sqrt{35}}{-280}
=\frac{\sqrt{35}}{-35}
$