75/m=7.5m=

Solution for 75/m=7.5m= equation:

75/m=7.5m=

We move all terms to the left:

75/m-(7.5m)=0


Domain of the equation: m!=0

m∈R


We add all the numbers together, and all the variables

75/m-(+7.5m)=0

We get rid of parentheses

75/m-7.5m=0

We multiply all the terms by the denominator


-(7.5m)*m+75=0

We add all the numbers together, and all the variables

-(+7.5m)*m+75=0

We multiply parentheses

-7m^2+75=0

a = -7; b = 0; c = +75;
Δ = b2-4ac
Δ = 02-4·(-7)·75
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{21}}{2*-7}=\frac{0-10\sqrt{21}}{-14}
=-\frac{10\sqrt{21}}{-14}
=-\frac{5\sqrt{21}}{-7}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{21}}{2*-7}=\frac{0+10\sqrt{21}}{-14}
=\frac{10\sqrt{21}}{-14}
=\frac{5\sqrt{21}}{-7}
$