.5x-2.5=5/4x+2

Solution for .5x-2.5=5/4x+2 equation:

.5x-2.5=5/4x+2

We move all terms to the left:

.5x-2.5-(5/4x+2)=0


Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

.5x-5/4x-2-2.5=0

We multiply all the terms by the denominator


(.5x)*4x-2*4x-(2.5)*4x-5=0

We add all the numbers together, and all the variables

(+.5x)*4x-2*4x-(2.5)*4x-5=0

We multiply parentheses

4x^2-2*4x-10x-5=0

Wy multiply elements

4x^2-8x-10x-5=0

We add all the numbers together, and all the variables

4x^2-18x-5=0

a = 4; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·4·(-5)
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{101}}{2*4}=\frac{18-2\sqrt{101}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{101}}{2*4}=\frac{18+2\sqrt{101}}{8}
$