2/5x+4=1.5x+8

Solution for 2/5x+4=1.5x+8 equation:

2/5x+4=1.5x+8

We move all terms to the left:

2/5x+4-(1.5x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-1.5x-8+4=0

We multiply all the terms by the denominator


-(1.5x)*5x-8*5x+4*5x+2=0

We add all the numbers together, and all the variables

-(+1.5x)*5x-8*5x+4*5x+2=0

We multiply parentheses

-5x^2-8*5x+4*5x+2=0

Wy multiply elements

-5x^2-40x+20x+2=0

We add all the numbers together, and all the variables

-5x^2-20x+2=0

a = -5; b = -20; c = +2;
Δ = b2-4ac
Δ = -202-4·(-5)·2
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{110}}{2*-5}=\frac{20-2\sqrt{110}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{110}}{2*-5}=\frac{20+2\sqrt{110}}{-10}
$