4x-3/2x+6=3

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

4x-3/2x+6=3

We move all terms to the left:

4x-3/2x+6-(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-3/2x+3=0

We multiply all the terms by the denominator


4x*2x+3*2x-3=0

Wy multiply elements

8x^2+6x-3=0

a = 8; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·8·(-3)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{33}}{2*8}=\frac{-6-2\sqrt{33}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*8}=\frac{-6+2\sqrt{33}}{16}
$