1-5x+2=3-2/7x

Solution for 1-5x+2=3-2/7x equation:

1-5x+2=3-2/7x

We move all terms to the left:

1-5x+2-(3-2/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-5x-(-2/7x+3)+1+2=0

We add all the numbers together, and all the variables

-5x-(-2/7x+3)+3=0

We get rid of parentheses

-5x+2/7x-3+3=0

We multiply all the terms by the denominator


-5x*7x-3*7x+3*7x+2=0

Wy multiply elements

-35x^2-21x+21x+2=0

We add all the numbers together, and all the variables

-35x^2+2=0

a = -35; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-35)·2
Δ = 280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{70}}{2*-35}=\frac{0-2\sqrt{70}}{-70}
=-\frac{2\sqrt{70}}{-70}
=-\frac{\sqrt{70}}{-35}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{70}}{2*-35}=\frac{0+2\sqrt{70}}{-70}
=\frac{2\sqrt{70}}{-70}
=\frac{\sqrt{70}}{-35}
$