(3/4)-(5/4)m=(113/24)

Solution for (3/4)-(5/4)m=(113/24) equation:

(3/4)-(5/4)m=(113/24)

We move all terms to the left:

(3/4)-(5/4)m-((113/24))=0


Domain of the equation: 4)m!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

-(+5/4)m+(+3/4)-((+113/24))=0

We multiply parentheses

-5m^2+(+3/4)-((+113/24))=0

We get rid of parentheses

-5m^2+3/4-((+113/24))=0

We calculate fractions


-5m^2+()/()+()/()=0

We add all the numbers together, and all the variables

-5m^2+2=0

a = -5; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-5)·2
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*-5}=\frac{0-2\sqrt{10}}{-10}
=-\frac{2\sqrt{10}}{-10}
=-\frac{\sqrt{10}}{-5}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*-5}=\frac{0+2\sqrt{10}}{-10}
=\frac{2\sqrt{10}}{-10}
=\frac{\sqrt{10}}{-5}
$