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

Solution for (x)=3x+2/5x-2 equation:

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2-15x^2+10x-2=0

We add all the numbers together, and all the variables

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

a = -10; b = 10; c = -2;
Δ = b2-4ac
Δ = 102-4·(-10)·(-2)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{5}}{2*-10}=\frac{-10-2\sqrt{5}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{5}}{2*-10}=\frac{-10+2\sqrt{5}}{-20}
$