1/5x^+6=2x

Solution for 1/5x^+6=2x equation:

1/5x^+6=2x

We move all terms to the left:

1/5x^+6-(2x)=0


Domain of the equation: 5x^!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+1/5x^+6=0

We multiply all the terms by the denominator


-2x*5x^+6*5x^+1=0

Wy multiply elements

-10x^2+30x+1=0

a = -10; b = 30; c = +1;
Δ = b2-4ac
Δ = 302-4·(-10)·1
Δ = 940
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:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{235}}{2*-10}=\frac{-30-2\sqrt{235}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{235}}{2*-10}=\frac{-30+2\sqrt{235}}{-20}
$