40/7.50m=12.50m

Solution for 40/7.50m=12.50m equation:

40/7.50m=12.50m

We move all terms to the left:

40/7.50m-(12.50m)=0


Domain of the equation: 7.50m!=0

m!=0/7.50

m!=0

m∈R


We add all the numbers together, and all the variables

40/7.50m-(+12.50m)=0

We get rid of parentheses

40/7.50m-12.50m=0

We multiply all the terms by the denominator


-(12.50m)*7.50m+40=0

We add all the numbers together, and all the variables

-(+12.50m)*7.50m+40=0

We multiply parentheses

-84m^2+40=0

a = -84; b = 0; c = +40;
Δ = b2-4ac
Δ = 02-4·(-84)·40
Δ = 13440
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:

$\sqrt{\Delta}=\sqrt{13440}=\sqrt{64*210}=\sqrt{64}*\sqrt{210}=8\sqrt{210}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{210}}{2*-84}=\frac{0-8\sqrt{210}}{-168}
=-\frac{8\sqrt{210}}{-168}
=-\frac{\sqrt{210}}{-21}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{210}}{2*-84}=\frac{0+8\sqrt{210}}{-168}
=\frac{8\sqrt{210}}{-168}
=\frac{\sqrt{210}}{-21}
$