3/2x-3=x+1.414

Solution for 3/2x-3=x+1.414 equation:

3/2x-3=x+1.414

We move all terms to the left:

3/2x-3-(x+1.414)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-x-1.414-3=0

We multiply all the terms by the denominator


-x*2x-(1.414)*2x-3*2x+3=0

We multiply parentheses

-x*2x-2.828x-3*2x+3=0

Wy multiply elements

-2x^2-2.828x-6x+3=0

We add all the numbers together, and all the variables

-2x^2-8.828x+3=0

a = -2; b = -8.828; c = +3;
Δ = b2-4ac
Δ = -8.8282-4·(-2)·3
Δ = 101.933584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8.828)-\sqrt{101.933584}}{2*-2}=\frac{8.828-\sqrt{101.933584}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.828)+\sqrt{101.933584}}{2*-2}=\frac{8.828+\sqrt{101.933584}}{-4}
$