0.8x-1.6=1/4x+1

Solution for 0.8x-1.6=1/4x+1 equation:

0.8x-1.6=1/4x+1

We move all terms to the left:

0.8x-1.6-(1/4x+1)=0


Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

0.8x-1/4x-1-1.6=0

We multiply all the terms by the denominator


(0.8x)*4x-1*4x-(1.6)*4x-1=0

We add all the numbers together, and all the variables

(+0.8x)*4x-1*4x-(1.6)*4x-1=0

We multiply parentheses

0x^2-1*4x-6.4x-1=0

Wy multiply elements

0x^2-4x-6.4x-1=0

We add all the numbers together, and all the variables

x^2-10.4x-1=0

a = 1; b = -10.4; c = -1;
Δ = b2-4ac
Δ = -10.42-4·1·(-1)
Δ = 112.16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10.4)-\sqrt{112.16}}{2*1}=\frac{10.4-\sqrt{112.16}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10.4)+\sqrt{112.16}}{2*1}=\frac{10.4+\sqrt{112.16}}{2}
$