2x+7=4/2x-7

Solution for 2x+7=4/2x-7 equation:

2x+7=4/2x-7

We move all terms to the left:

2x+7-(4/2x-7)=0


Domain of the equation: 2x-7)!=0

x∈R


We get rid of parentheses

2x-4/2x+7+7=0

We multiply all the terms by the denominator


2x*2x+7*2x+7*2x-4=0

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2+28x-4=0

a = 4; b = 28; c = -4;
Δ = b2-4ac
Δ = 282-4·4·(-4)
Δ = 848
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:

$\sqrt{\Delta}=\sqrt{848}=\sqrt{16*53}=\sqrt{16}*\sqrt{53}=4\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{53}}{2*4}=\frac{-28-4\sqrt{53}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{53}}{2*4}=\frac{-28+4\sqrt{53}}{8}
$