7/2x-19=13+2x

Solution for 7/2x-19=13+2x equation:

7/2x-19=13+2x

We move all terms to the left:

7/2x-19-(13+2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

7/2x-(2x+13)-19=0

We get rid of parentheses

7/2x-2x-13-19=0

We multiply all the terms by the denominator


-2x*2x-13*2x-19*2x+7=0

Wy multiply elements

-4x^2-26x-38x+7=0

We add all the numbers together, and all the variables

-4x^2-64x+7=0

a = -4; b = -64; c = +7;
Δ = b2-4ac
Δ = -642-4·(-4)·7
Δ = 4208
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:

$\sqrt{\Delta}=\sqrt{4208}=\sqrt{16*263}=\sqrt{16}*\sqrt{263}=4\sqrt{263}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{263}}{2*-4}=\frac{64-4\sqrt{263}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{263}}{2*-4}=\frac{64+4\sqrt{263}}{-8}
$