1/4x+17=3x-5

Solution for 1/4x+17=3x-5 equation:

1/4x+17=3x-5

We move all terms to the left:

1/4x+17-(3x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-3x+5+17=0

We multiply all the terms by the denominator


-3x*4x+5*4x+17*4x+1=0

Wy multiply elements

-12x^2+20x+68x+1=0

We add all the numbers together, and all the variables

-12x^2+88x+1=0

a = -12; b = 88; c = +1;
Δ = b2-4ac
Δ = 882-4·(-12)·1
Δ = 7792
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:

$\sqrt{\Delta}=\sqrt{7792}=\sqrt{16*487}=\sqrt{16}*\sqrt{487}=4\sqrt{487}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-4\sqrt{487}}{2*-12}=\frac{-88-4\sqrt{487}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+4\sqrt{487}}{2*-12}=\frac{-88+4\sqrt{487}}{-24}
$