5x+20=1/2x-6

Solution for 5x+20=1/2x-6 equation:

5x+20=1/2x-6

We move all terms to the left:

5x+20-(1/2x-6)=0


Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

5x-1/2x+6+20=0

We multiply all the terms by the denominator


5x*2x+6*2x+20*2x-1=0

Wy multiply elements

10x^2+12x+40x-1=0

We add all the numbers together, and all the variables

10x^2+52x-1=0

a = 10; b = 52; c = -1;
Δ = b2-4ac
Δ = 522-4·10·(-1)
Δ = 2744
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:

$\sqrt{\Delta}=\sqrt{2744}=\sqrt{196*14}=\sqrt{196}*\sqrt{14}=14\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-14\sqrt{14}}{2*10}=\frac{-52-14\sqrt{14}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+14\sqrt{14}}{2*10}=\frac{-52+14\sqrt{14}}{20}
$