-6x+10=1/2x

Solution for -6x+10=1/2x equation:

-6x+10=1/2x

We move all terms to the left:

-6x+10-(1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-6x-(+1/2x)+10=0

We get rid of parentheses

-6x-1/2x+10=0

We multiply all the terms by the denominator


-6x*2x+10*2x-1=0

Wy multiply elements

-12x^2+20x-1=0

a = -12; b = 20; c = -1;
Δ = b2-4ac
Δ = 202-4·(-12)·(-1)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{22}}{2*-12}=\frac{-20-4\sqrt{22}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{22}}{2*-12}=\frac{-20+4\sqrt{22}}{-24}
$