2x+15/4x-5=3

Solution for 2x+15/4x-5=3 equation:

2x+15/4x-5=3

We move all terms to the left:

2x+15/4x-5-(3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+15/4x-8=0

We multiply all the terms by the denominator


2x*4x-8*4x+15=0

Wy multiply elements

8x^2-32x+15=0

a = 8; b = -32; c = +15;
Δ = b2-4ac
Δ = -322-4·8·15
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{34}}{2*8}=\frac{32-4\sqrt{34}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{34}}{2*8}=\frac{32+4\sqrt{34}}{16}
$