2x+5=2/5x+7.5

Solution for 2x+5=2/5x+7.5 equation:

2x+5=2/5x+7.5

We move all terms to the left:

2x+5-(2/5x+7.5)=0


Domain of the equation: 5x+7.5)!=0

x∈R


We get rid of parentheses

2x-2/5x-7.5+5=0

We multiply all the terms by the denominator


2x*5x-(7.5)*5x+5*5x-2=0

We multiply parentheses

2x*5x-37.5x+5*5x-2=0

Wy multiply elements

10x^2-37.5x+25x-2=0

We add all the numbers together, and all the variables

10x^2-12.5x-2=0

a = 10; b = -12.5; c = -2;
Δ = b2-4ac
Δ = -12.52-4·10·(-2)
Δ = 236.25
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{-(-12.5)-\sqrt{236.25}}{2*10}=\frac{12.5-\sqrt{236.25}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12.5)+\sqrt{236.25}}{2*10}=\frac{12.5+\sqrt{236.25}}{20}
$