1/2x=x+30

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

1/2x=x+30

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-x-30=0

We multiply all the terms by the denominator


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

Wy multiply elements

-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}
$