5/4x+3=4x-17

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

5/4x+3=4x-17

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-16x^2+68x+12x+5=0

We add all the numbers together, and all the variables

-16x^2+80x+5=0

a = -16; b = 80; c = +5;
Δ = b2-4ac
Δ = 802-4·(-16)·5
Δ = 6720
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:

$\sqrt{\Delta}=\sqrt{6720}=\sqrt{64*105}=\sqrt{64}*\sqrt{105}=8\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-8\sqrt{105}}{2*-16}=\frac{-80-8\sqrt{105}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+8\sqrt{105}}{2*-16}=\frac{-80+8\sqrt{105}}{-32}
$