7/10x+3/5=5/6x+1

Solution for 7/10x+3/5=5/6x+1 equation:

7/10x+3/5=5/6x+1

We move all terms to the left:

7/10x+3/5-(5/6x+1)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 6x+1)!=0

x∈R


We get rid of parentheses

7/10x-5/6x-1+3/5=0

We calculate fractions


1080x^2/1500x^2+1050x/1500x^2+(-1250x)/1500x^2-1=0

We multiply all the terms by the denominator


1080x^2+1050x+(-1250x)-1*1500x^2=0

Wy multiply elements

1080x^2-1500x^2+1050x+(-1250x)=0

We get rid of parentheses

1080x^2-1500x^2+1050x-1250x=0

We add all the numbers together, and all the variables

-420x^2-200x=0

a = -420; b = -200; c = 0;
Δ = b2-4ac
Δ = -2002-4·(-420)·0
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-200}{2*-420}=\frac{0}{-840}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+200}{2*-420}=\frac{400}{-840}
=-10/21
$