7/2x+2x-9=26

Solution for 7/2x+2x-9=26 equation:

7/2x+2x-9=26

We move all terms to the left:

7/2x+2x-9-(26)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+7/2x-35=0

We multiply all the terms by the denominator


2x*2x-35*2x+7=0

Wy multiply elements

4x^2-70x+7=0

a = 4; b = -70; c = +7;
Δ = b2-4ac
Δ = -702-4·4·7
Δ = 4788
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:

$\sqrt{\Delta}=\sqrt{4788}=\sqrt{36*133}=\sqrt{36}*\sqrt{133}=6\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-6\sqrt{133}}{2*4}=\frac{70-6\sqrt{133}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+6\sqrt{133}}{2*4}=\frac{70+6\sqrt{133}}{8}
$