1/5x+1=0.75x+12

Solution for 1/5x+1=0.75x+12 equation:

1/5x+1=0.75x+12

We move all terms to the left:

1/5x+1-(0.75x+12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-0.75x-12+1=0

We multiply all the terms by the denominator


-(0.75x)*5x-12*5x+1*5x+1=0

We add all the numbers together, and all the variables

-(+0.75x)*5x-12*5x+1*5x+1=0

We multiply parentheses

-0x^2-12*5x+1*5x+1=0

Wy multiply elements

-0x^2-60x+5x+1=0

We add all the numbers together, and all the variables

-1x^2-55x+1=0

a = -1; b = -55; c = +1;
Δ = b2-4ac
Δ = -552-4·(-1)·1
Δ = 3029
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{-(-55)-\sqrt{3029}}{2*-1}=\frac{55-\sqrt{3029}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{3029}}{2*-1}=\frac{55+\sqrt{3029}}{-2}
$