4x*4-6x*3-2x*2+4x+42/2x+3=0

Solution for 4x*4-6x*3-2x*2+4x+42/2x+3=0 equation:

4x*4-6x*3-2x*2+4x+42/2x+3=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x+4x*4-6x*3-2x*2+42/2x+3=0

Wy multiply elements

4x+16x-18x-4x+42/2x+3=0

We multiply all the terms by the denominator


4x*2x+16x*2x-18x*2x-4x*2x+3*2x+42=0

Wy multiply elements

8x^2+32x^2-36x^2-8x^2+6x+42=0

We add all the numbers together, and all the variables

-4x^2+6x+42=0

a = -4; b = 6; c = +42;
Δ = b2-4ac
Δ = 62-4·(-4)·42
Δ = 708
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:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{177}}{2*-4}=\frac{-6-2\sqrt{177}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{177}}{2*-4}=\frac{-6+2\sqrt{177}}{-8}
$