2x+2/5x-1=12-7x

Solution for 2x+2/5x-1=12-7x equation:

2x+2/5x-1=12-7x

We move all terms to the left:

2x+2/5x-1-(12-7x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2x+2/5x-(-7x+12)-1=0

We get rid of parentheses

2x+2/5x+7x-12-1=0

We multiply all the terms by the denominator


2x*5x+7x*5x-12*5x-1*5x+2=0

Wy multiply elements

10x^2+35x^2-60x-5x+2=0

We add all the numbers together, and all the variables

45x^2-65x+2=0

a = 45; b = -65; c = +2;
Δ = b2-4ac
Δ = -652-4·45·2
Δ = 3865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-\sqrt{3865}}{2*45}=\frac{65-\sqrt{3865}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{3865}}{2*45}=\frac{65+\sqrt{3865}}{90}
$