1/2x+1/2x+30=6x

Solution for 1/2x+1/2x+30=6x equation:

1/2x+1/2x+30=6x

We move all terms to the left:

1/2x+1/2x+30-(6x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+1/2x+1/2x+30=0

We multiply all the terms by the denominator


-6x*2x+30*2x+1+1=0

We add all the numbers together, and all the variables

-6x*2x+30*2x+2=0

Wy multiply elements

-12x^2+60x+2=0

a = -12; b = 60; c = +2;
Δ = b2-4ac
Δ = 602-4·(-12)·2
Δ = 3696
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:

$\sqrt{\Delta}=\sqrt{3696}=\sqrt{16*231}=\sqrt{16}*\sqrt{231}=4\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{231}}{2*-12}=\frac{-60-4\sqrt{231}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{231}}{2*-12}=\frac{-60+4\sqrt{231}}{-24}
$