1.6x-x+4=2/5x-8

Solution for 1.6x-x+4=2/5x-8 equation:

1.6x-x+4=2/5x-8

We move all terms to the left:

1.6x-x+4-(2/5x-8)=0


Domain of the equation: 5x-8)!=0

x∈R


We add all the numbers together, and all the variables

0.6x-(2/5x-8)+4=0

We get rid of parentheses

0.6x-2/5x+8+4=0

We multiply all the terms by the denominator


(0.6x)*5x+8*5x+4*5x-2=0

We add all the numbers together, and all the variables

(+0.6x)*5x+8*5x+4*5x-2=0

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

x^2+60x-2=0

a = 1; b = 60; c = -2;
Δ = b2-4ac
Δ = 602-4·1·(-2)
Δ = 3608
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:

$\sqrt{\Delta}=\sqrt{3608}=\sqrt{4*902}=\sqrt{4}*\sqrt{902}=2\sqrt{902}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{902}}{2*1}=\frac{-60-2\sqrt{902}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{902}}{2*1}=\frac{-60+2\sqrt{902}}{2}
$