1/2x-1.0676=3x-4.145

Solution for 1/2x-1.0676=3x-4.145 equation:

1/2x-1.0676=3x-4.145

We move all terms to the left:

1/2x-1.0676-(3x-4.145)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-3x+4.145-1.0676=0

We multiply all the terms by the denominator


-3x*2x+(4.145)*2x-(1.0676)*2x+1=0

We multiply parentheses

-3x*2x+8.29x-2.1352x+1=0

Wy multiply elements

-6x^2+8.29x-2.1352x+1=0

We add all the numbers together, and all the variables

-6x^2+6.1548x+1=0

a = -6; b = 6.1548; c = +1;
Δ = b2-4ac
Δ = 6.15482-4·(-6)·1
Δ = 61.88156304
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{-(6.1548)-\sqrt{61.88156304}}{2*-6}=\frac{-6.1548-\sqrt{61.88156304}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6.1548)+\sqrt{61.88156304}}{2*-6}=\frac{-6.1548+\sqrt{61.88156304}}{-12}
$