1/4x-1.75=1+3x

Solution for 1/4x-1.75=1+3x equation:

1/4x-1.75=1+3x

We move all terms to the left:

1/4x-1.75-(1+3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(3x+1)-1.75=0

We get rid of parentheses

1/4x-3x-1-1.75=0

We multiply all the terms by the denominator


-3x*4x-1*4x-(1.75)*4x+1=0

We multiply parentheses

-3x*4x-1*4x-7x+1=0

Wy multiply elements

-12x^2-4x-7x+1=0

We add all the numbers together, and all the variables

-12x^2-11x+1=0

a = -12; b = -11; c = +1;
Δ = b2-4ac
Δ = -112-4·(-12)·1
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-13}{2*-12}=\frac{-2}{-24}
=1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+13}{2*-12}=\frac{24}{-24}
=-1
$