1/2x+30+4x=-2x+14x+6

Solution for 1/2x+30+4x=-2x+14x+6 equation:

1/2x+30+4x=-2x+14x+6

We move all terms to the left:

1/2x+30+4x-(-2x+14x+6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+4x-(12x+6)+30=0

We add all the numbers together, and all the variables

4x+1/2x-(12x+6)+30=0

We get rid of parentheses

4x+1/2x-12x-6+30=0

We multiply all the terms by the denominator


4x*2x-12x*2x-6*2x+30*2x+1=0

Wy multiply elements

8x^2-24x^2-12x+60x+1=0

We add all the numbers together, and all the variables

-16x^2+48x+1=0

a = -16; b = 48; c = +1;
Δ = b2-4ac
Δ = 482-4·(-16)·1
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{37}}{2*-16}=\frac{-48-8\sqrt{37}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{37}}{2*-16}=\frac{-48+8\sqrt{37}}{-32}
$