2x+7=1/22x-2.5

Solution for 2x+7=1/22x-2.5 equation:

2x+7=1/22x-2.5

We move all terms to the left:

2x+7-(1/22x-2.5)=0


Domain of the equation: 22x-2.5)!=0

x∈R


We get rid of parentheses

2x-1/22x+2.5+7=0

We multiply all the terms by the denominator


2x*22x+(2.5)*22x+7*22x-1=0

We multiply parentheses

2x*22x+55x+7*22x-1=0

Wy multiply elements

44x^2+55x+154x-1=0

We add all the numbers together, and all the variables

44x^2+209x-1=0

a = 44; b = 209; c = -1;
Δ = b2-4ac
Δ = 2092-4·44·(-1)
Δ = 43857
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:

$\sqrt{\Delta}=\sqrt{43857}=\sqrt{9*4873}=\sqrt{9}*\sqrt{4873}=3\sqrt{4873}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(209)-3\sqrt{4873}}{2*44}=\frac{-209-3\sqrt{4873}}{88}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(209)+3\sqrt{4873}}{2*44}=\frac{-209+3\sqrt{4873}}{88}
$