X2+1=2+3x/2

Solution for X2+1=2+3x/2 equation:

X2+1=2+3X/2

We move all terms to the left:

X2+1-(2+3X/2)=0

We add all the numbers together, and all the variables

X2-(3X/2+2)+1=0

We add all the numbers together, and all the variables

X^2-(3X/2+2)+1=0

We get rid of parentheses

X^2-3X/2-2+1=0

We multiply all the terms by the denominator


X^2*2-3X-2*2+1*2=0

We add all the numbers together, and all the variables

X^2*2-3X-2=0

Wy multiply elements

2X^2-3X-2=0

a = 2; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·2·(-2)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*2}=\frac{-2}{4}
=-1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*2}=\frac{8}{4}
=2
$