-15/(4x+1)=x-4

Solution for -15/(4x+1)=x-4 equation:

-15/(4x+1)=x-4

We move all terms to the left:

-15/(4x+1)-(x-4)=0


Domain of the equation: (4x+1)!=0

We move all terms containing x to the left, all other terms to the right

4x!=-1

x!=-1/4

x!=-1/4

x∈R


We get rid of parentheses

-15/(4x+1)-x+4=0

We multiply all the terms by the denominator


-x*(4x+1)+4*(4x+1)-15=0

We multiply parentheses

-4x^2-x+16x+4-15=0

We add all the numbers together, and all the variables

-4x^2+15x-11=0

a = -4; b = 15; c = -11;
Δ = b2-4ac
Δ = 152-4·(-4)·(-11)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-7}{2*-4}=\frac{-22}{-8}
=2+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+7}{2*-4}=\frac{-8}{-8}
=1
$