1/2x-2.5=2x+5

Solution for 1/2x-2.5=2x+5 equation:

1/2x-2.5=2x+5

We move all terms to the left:

1/2x-2.5-(2x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-2x-5-2.5=0

We multiply all the terms by the denominator


-2x*2x-5*2x-(2.5)*2x+1=0

We multiply parentheses

-2x*2x-5*2x-5x+1=0

Wy multiply elements

-4x^2-10x-5x+1=0

We add all the numbers together, and all the variables

-4x^2-15x+1=0

a = -4; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·(-4)·1
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{241}}{2*-4}=\frac{15-\sqrt{241}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{241}}{2*-4}=\frac{15+\sqrt{241}}{-8}
$