1/2x=1.8x+1.4

Solution for 1/2x=1.8x+1.4 equation:

1/2x=1.8x+1.4

We move all terms to the left:

1/2x-(1.8x+1.4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-1.8x-1.4=0

We multiply all the terms by the denominator


-(1.8x)*2x-(1.4)*2x+1=0

We add all the numbers together, and all the variables

-(+1.8x)*2x-(1.4)*2x+1=0

We multiply parentheses

-2x^2-2.8x+1=0

a = -2; b = -2.8; c = +1;
Δ = b2-4ac
Δ = -2.82-4·(-2)·1
Δ = 15.84
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{-(-2.8)-\sqrt{15.84}}{2*-2}=\frac{2.8-\sqrt{15.84}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.8)+\sqrt{15.84}}{2*-2}=\frac{2.8+\sqrt{15.84}}{-4}
$