3/4m-10=m-4

Solution for 3/4m-10=m-4 equation:

3/4m-10=m-4

We move all terms to the left:

3/4m-10-(m-4)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We get rid of parentheses

3/4m-m+4-10=0

We multiply all the terms by the denominator


-m*4m+4*4m-10*4m+3=0

Wy multiply elements

-4m^2+16m-40m+3=0

We add all the numbers together, and all the variables

-4m^2-24m+3=0

a = -4; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·(-4)·3
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{39}}{2*-4}=\frac{24-4\sqrt{39}}{-8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{39}}{2*-4}=\frac{24+4\sqrt{39}}{-8}
$