2.5x+5=1/2x+25

Solution for 2.5x+5=1/2x+25 equation:

2.5x+5=1/2x+25

We move all terms to the left:

2.5x+5-(1/2x+25)=0


Domain of the equation: 2x+25)!=0

x∈R


We get rid of parentheses

2.5x-1/2x-25+5=0

We multiply all the terms by the denominator


(2.5x)*2x-25*2x+5*2x-1=0

We add all the numbers together, and all the variables

(+2.5x)*2x-25*2x+5*2x-1=0

We multiply parentheses

4x^2-25*2x+5*2x-1=0

Wy multiply elements

4x^2-50x+10x-1=0

We add all the numbers together, and all the variables

4x^2-40x-1=0

a = 4; b = -40; c = -1;
Δ = b2-4ac
Δ = -402-4·4·(-1)
Δ = 1616
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:

$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{101}}{2*4}=\frac{40-4\sqrt{101}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{101}}{2*4}=\frac{40+4\sqrt{101}}{8}
$