3x2-5x/2-2=x2+1

Solution for 3x2-5x/2-2=x2+1 equation:

3x^2-5x/2-2=x2+1

We move all terms to the left:

3x^2-5x/2-2-(x2+1)=0

We add all the numbers together, and all the variables

3x^2-(+x^2+1)-5x/2-2=0

We get rid of parentheses

3x^2-x^2-5x/2-1-2=0

We multiply all the terms by the denominator


3x^2*2-x^2*2-5x-1*2-2*2=0

We add all the numbers together, and all the variables

3x^2*2-x^2*2-5x-6=0

Wy multiply elements

6x^2-2x^2-5x-6=0

We add all the numbers together, and all the variables

4x^2-5x-6=0

a = 4; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·4·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*4}=\frac{-6}{8}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*4}=\frac{16}{8}
=2
$