2x+7=1/5x-2

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

2x+7=1/5x-2

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2+10x+35x-1=0

We add all the numbers together, and all the variables

10x^2+45x-1=0

a = 10; b = 45; c = -1;
Δ = b2-4ac
Δ = 452-4·10·(-1)
Δ = 2065
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{-(45)-\sqrt{2065}}{2*10}=\frac{-45-\sqrt{2065}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2065}}{2*10}=\frac{-45+\sqrt{2065}}{20}
$