2x+30=1/2x+x

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

2x+30=1/2x+x

We move all terms to the left:

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


Domain of the equation: 2x+x)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-2x^2+60x-1=0

We add all the numbers together, and all the variables

2x^2+60x-1=0

a = 2; b = 60; c = -1;
Δ = b2-4ac
Δ = 602-4·2·(-1)
Δ = 3608
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:

$\sqrt{\Delta}=\sqrt{3608}=\sqrt{4*902}=\sqrt{4}*\sqrt{902}=2\sqrt{902}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{902}}{2*2}=\frac{-60-2\sqrt{902}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{902}}{2*2}=\frac{-60+2\sqrt{902}}{4}
$