2.6x+5/4x-23=33

Solution for 2.6x+5/4x-23=33 equation:

2.6x+5/4x-23=33

We move all terms to the left:

2.6x+5/4x-23-(33)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2.6x+5/4x-56=0

We multiply all the terms by the denominator


(2.6x)*4x-56*4x+5=0

We add all the numbers together, and all the variables

(+2.6x)*4x-56*4x+5=0

We multiply parentheses

8x^2-56*4x+5=0

Wy multiply elements

8x^2-224x+5=0

a = 8; b = -224; c = +5;
Δ = b2-4ac
Δ = -2242-4·8·5
Δ = 50016
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:

$\sqrt{\Delta}=\sqrt{50016}=\sqrt{16*3126}=\sqrt{16}*\sqrt{3126}=4\sqrt{3126}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-224)-4\sqrt{3126}}{2*8}=\frac{224-4\sqrt{3126}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-224)+4\sqrt{3126}}{2*8}=\frac{224+4\sqrt{3126}}{16}
$