2x+7=17/2x+9=19

Solution for 2x+7=17/2x+9=19 equation:

2x+7=17/2x+9=19

We move all terms to the left:

2x+7-(17/2x+9)=0


Domain of the equation: 2x+9)!=0

x∈R


We get rid of parentheses

2x-17/2x-9+7=0

We multiply all the terms by the denominator


2x*2x-9*2x+7*2x-17=0

Wy multiply elements

4x^2-18x+14x-17=0

We add all the numbers together, and all the variables

4x^2-4x-17=0

a = 4; b = -4; c = -17;
Δ = b2-4ac
Δ = -42-4·4·(-17)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12\sqrt{2}}{2*4}=\frac{4-12\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12\sqrt{2}}{2*4}=\frac{4+12\sqrt{2}}{8}
$