(3x^2+3x)/2=84

Solution for (3x^2+3x)/2=84 equation:

(3x^2+3x)/2=84

We move all terms to the left:

(3x^2+3x)/2-(84)=0

We multiply all the terms by the denominator


(3x^2+3x)-84*2=0

We add all the numbers together, and all the variables

(3x^2+3x)-168=0

We get rid of parentheses

3x^2+3x-168=0

a = 3; b = 3; c = -168;
Δ = b2-4ac
Δ = 32-4·3·(-168)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-45}{2*3}=\frac{-48}{6}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+45}{2*3}=\frac{42}{6}
=7
$