1/2x=3x-3.5

Solution for 1/2x=3x-3.5 equation:

1/2x=3x-3.5

We move all terms to the left:

1/2x-(3x-3.5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-3x+3.5=0

We multiply all the terms by the denominator


-3x*2x+(3.5)*2x+1=0

We multiply parentheses

-3x*2x+7x+1=0

Wy multiply elements

-6x^2+7x+1=0

a = -6; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·(-6)·1
Δ = 73
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{-(7)-\sqrt{73}}{2*-6}=\frac{-7-\sqrt{73}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{73}}{2*-6}=\frac{-7+\sqrt{73}}{-12}
$