4x^2-4x-3x-4x^2+2x-7/3x=-1+23

Solution for 4x^2-4x-3x-4x^2+2x-7/3x=-1+23 equation:

4x^2-4x-3x-4x^2+2x-7/3x=-1+23

We move all terms to the left:

4x^2-4x-3x-4x^2+2x-7/3x-(-1+23)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4x^2-4x^2-4x-3x+2x-7/3x-22=0

We add all the numbers together, and all the variables

-5x-7/3x-22=0

We multiply all the terms by the denominator


-5x*3x-22*3x-7=0

Wy multiply elements

-15x^2-66x-7=0

a = -15; b = -66; c = -7;
Δ = b2-4ac
Δ = -662-4·(-15)·(-7)
Δ = 3936
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:

$\sqrt{\Delta}=\sqrt{3936}=\sqrt{16*246}=\sqrt{16}*\sqrt{246}=4\sqrt{246}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-4\sqrt{246}}{2*-15}=\frac{66-4\sqrt{246}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+4\sqrt{246}}{2*-15}=\frac{66+4\sqrt{246}}{-30}
$