6/25x+7.5-2.5x=3.75x-8.75

Solution for 6/25x+7.5-2.5x=3.75x-8.75 equation:

6/25x+7.5-2.5x=3.75x-8.75

We move all terms to the left:

6/25x+7.5-2.5x-(3.75x-8.75)=0


Domain of the equation: 25x!=0

x!=0/25

x!=0

x∈R


We add all the numbers together, and all the variables

-2.5x+6/25x-(3.75x-8.75)+7.5=0

We get rid of parentheses

-2.5x+6/25x-3.75x+8.75+7.5=0

We multiply all the terms by the denominator


-(2.5x)*25x-(3.75x)*25x+(8.75)*25x+(7.5)*25x+6=0

We add all the numbers together, and all the variables

-(+2.5x)*25x-(+3.75x)*25x+(8.75)*25x+(7.5)*25x+6=0

We multiply parentheses

-50x^2-75x^2+218.75x+187.5x+6=0

We add all the numbers together, and all the variables

-125x^2+406.25x+6=0

a = -125; b = 406.25; c = +6;
Δ = b2-4ac
Δ = 406.252-4·(-125)·6
Δ = 168039.0625
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{-(406.25)-\sqrt{168039.0625}}{2*-125}=\frac{-406.25-\sqrt{168039.0625}}{-250}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(406.25)+\sqrt{168039.0625}}{2*-125}=\frac{-406.25+\sqrt{168039.0625}}{-250}
$