3/4x+16=5x-1

Solution for 3/4x+16=5x-1 equation:

3/4x+16=5x-1

We move all terms to the left:

3/4x+16-(5x-1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-5x+1+16=0

We multiply all the terms by the denominator


-5x*4x+1*4x+16*4x+3=0

Wy multiply elements

-20x^2+4x+64x+3=0

We add all the numbers together, and all the variables

-20x^2+68x+3=0

a = -20; b = 68; c = +3;
Δ = b2-4ac
Δ = 682-4·(-20)·3
Δ = 4864
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:

$\sqrt{\Delta}=\sqrt{4864}=\sqrt{256*19}=\sqrt{256}*\sqrt{19}=16\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-16\sqrt{19}}{2*-20}=\frac{-68-16\sqrt{19}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+16\sqrt{19}}{2*-20}=\frac{-68+16\sqrt{19}}{-40}
$