100/2x+3=2x+7

Solution for 100/2x+3=2x+7 equation:

100/2x+3=2x+7

We move all terms to the left:

100/2x+3-(2x+7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

100/2x-2x-7+3=0

We multiply all the terms by the denominator


-2x*2x-7*2x+3*2x+100=0

Wy multiply elements

-4x^2-14x+6x+100=0

We add all the numbers together, and all the variables

-4x^2-8x+100=0

a = -4; b = -8; c = +100;
Δ = b2-4ac
Δ = -82-4·(-4)·100
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{26}}{2*-4}=\frac{8-8\sqrt{26}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{26}}{2*-4}=\frac{8+8\sqrt{26}}{-8}
$