69=3(x^2-2)

Solution for 69=3(x^2-2) equation:

69=3(x^2-2)

We move all terms to the left:

69-(3(x^2-2))=0


We calculate terms in parentheses: -(3(x^2-2)), so:

3(x^2-2)

We multiply parentheses

3x^2-6

Back to the equation:

-(3x^2-6)


We get rid of parentheses

-3x^2+6+69=0

We add all the numbers together, and all the variables

-3x^2+75=0

a = -3; b = 0; c = +75;
Δ = b2-4ac
Δ = 02-4·(-3)·75
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*-3}=\frac{30}{-6}
=-5
$