X+2/5x=2x-6

Solution for X+2/5x=2x-6 equation:

X+2/5X=2X-6

We move all terms to the left:

X+2/5X-(2X-6)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We get rid of parentheses

X+2/5X-2X+6=0

We multiply all the terms by the denominator


X*5X-2X*5X+6*5X+2=0

Wy multiply elements

5X^2-10X^2+30X+2=0

We add all the numbers together, and all the variables

-5X^2+30X+2=0

a = -5; b = 30; c = +2;
Δ = b2-4ac
Δ = 302-4·(-5)·2
Δ = 940
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:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{235}}{2*-5}=\frac{-30-2\sqrt{235}}{-10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{235}}{2*-5}=\frac{-30+2\sqrt{235}}{-10}
$