X-3(2-4/5x)=1/2x

Solution for X-3(2-4/5x)=1/2x equation:

X-3(2-4/5X)=1/2X

We move all terms to the left:

X-3(2-4/5X)-(1/2X)=0


Domain of the equation: 5X)!=0

X!=0/1

X!=0

X∈R



Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-3(-4/5X+2)-(+1/2X)=0

We multiply parentheses

X+12X-(+1/2X)-6=0

We get rid of parentheses

X+12X-1/2X-6=0

We multiply all the terms by the denominator


X*2X+12X*2X-6*2X-1=0

Wy multiply elements

2X^2+24X^2-12X-1=0

We add all the numbers together, and all the variables

26X^2-12X-1=0

a = 26; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·26·(-1)
Δ = 248
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:

$\sqrt{\Delta}=\sqrt{248}=\sqrt{4*62}=\sqrt{4}*\sqrt{62}=2\sqrt{62}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{62}}{2*26}=\frac{12-2\sqrt{62}}{52}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{62}}{2*26}=\frac{12+2\sqrt{62}}{52}
$