3/4m=15,m=

Solution for 3/4m=15,m= equation:

3/4m=15.m=

We move all terms to the left:

3/4m-(15.m)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We add all the numbers together, and all the variables

3/4m-(+15.m)=0

We get rid of parentheses

3/4m-15.m=0

We multiply all the terms by the denominator


-(15.m)*4m+3=0

We add all the numbers together, and all the variables

-(+15.m)*4m+3=0

We multiply parentheses

-60m^2+3=0

a = -60; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-60)·3
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*-60}=\frac{0-12\sqrt{5}}{-120}
=-\frac{12\sqrt{5}}{-120}
=-\frac{\sqrt{5}}{-10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*-60}=\frac{0+12\sqrt{5}}{-120}
=\frac{12\sqrt{5}}{-120}
=\frac{\sqrt{5}}{-10}
$