X^2-7=3x/2

Solution for X^2-7=3x/2 equation:

X^2-7=3X/2

We move all terms to the left:

X^2-7-(3X/2)=0

We add all the numbers together, and all the variables

X^2-(+3X/2)-7=0

We get rid of parentheses

X^2-3X/2-7=0

We multiply all the terms by the denominator


X^2*2-3X-7*2=0

We add all the numbers together, and all the variables

X^2*2-3X-14=0

Wy multiply elements

2X^2-3X-14=0

a = 2; b = -3; c = -14;
Δ = b2-4ac
Δ = -32-4·2·(-14)
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{-(-3)-11}{2*2}=\frac{-8}{4}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+11}{2*2}=\frac{14}{4}
=3+1/2
$