3/4m-7/10=4/5m-2

Solution for 3/4m-7/10=4/5m-2 equation:

3/4m-7/10=4/5m-2

We move all terms to the left:

3/4m-7/10-(4/5m-2)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 5m-2)!=0

m∈R


We get rid of parentheses

3/4m-4/5m+2-7/10=0

We calculate fractions


(-700m^2)/200m^2+150m/200m^2+(-160m)/200m^2+2=0

We multiply all the terms by the denominator


(-700m^2)+150m+(-160m)+2*200m^2=0

Wy multiply elements

(-700m^2)+400m^2+150m+(-160m)=0

We get rid of parentheses

-700m^2+400m^2+150m-160m=0

We add all the numbers together, and all the variables

-300m^2-10m=0

a = -300; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-300)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-300}=\frac{0}{-600}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-300}=\frac{20}{-600}
=-1/30
$