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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6X+(X^2-7)=0

We get rid of parentheses

X^2-6X-7=0

a = 1; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·1·(-7)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8}{2*1}=\frac{14}{2}
=7
$