4x+3/2x-1=6

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Solution for 4x+3/2x-1=6 equation: 



4x+3/2x-1=6

We move all terms to the left:

4x+3/2x-1-(6)=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-7=0

We multiply all the terms by the denominator


4x*2x-7*2x+3=0

Wy multiply elements

8x^2-14x+3=0

a = 8; b = -14; c = +3;
Δ = b2-4ac
Δ = -142-4·8·3
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10}{2*8}=\frac{4}{16}
=1/4
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*8}=\frac{24}{16}
=1+1/2
$

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