7x-1/2x+7=2x-20

Solution for 7x-1/2x+7=2x-20 equation:

7x-1/2x+7=2x-20

We move all terms to the left:

7x-1/2x+7-(2x-20)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

7x-1/2x-2x+20+7=0

We multiply all the terms by the denominator


7x*2x-2x*2x+20*2x+7*2x-1=0

Wy multiply elements

14x^2-4x^2+40x+14x-1=0

We add all the numbers together, and all the variables

10x^2+54x-1=0

a = 10; b = 54; c = -1;
Δ = b2-4ac
Δ = 542-4·10·(-1)
Δ = 2956
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:

$\sqrt{\Delta}=\sqrt{2956}=\sqrt{4*739}=\sqrt{4}*\sqrt{739}=2\sqrt{739}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{739}}{2*10}=\frac{-54-2\sqrt{739}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{739}}{2*10}=\frac{-54+2\sqrt{739}}{20}
$