1/2x+5/6-3/10x=3/4

Solution for 1/2x+5/6-3/10x=3/4 equation:

1/2x+5/6-3/10x=3/4

We move all terms to the left:

1/2x+5/6-3/10x-(3/4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-3/10x+5/6-(+3/4)=0

We get rid of parentheses

1/2x-3/10x+5/6-3/4=0

We calculate fractions


(-360x^2)/2880x^2+400x^2/2880x^2+1440x/2880x^2+(-864x)/2880x^2=0

We multiply all the terms by the denominator


(-360x^2)+400x^2+1440x+(-864x)=0

We add all the numbers together, and all the variables

400x^2+(-360x^2)+1440x+(-864x)=0

We get rid of parentheses

400x^2-360x^2+1440x-864x=0

We add all the numbers together, and all the variables

40x^2+576x=0

a = 40; b = 576; c = 0;
Δ = b2-4ac
Δ = 5762-4·40·0
Δ = 331776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{331776}=576$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(576)-576}{2*40}=\frac{-1152}{80}
=-14+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(576)+576}{2*40}=\frac{0}{80}
=0
$