(3r2/2)+43=139

Solution for (3r2/2)+43=139 equation:

(3r^2/2)+43=139

We move all terms to the left:

(3r^2/2)+43-(139)=0

We add all the numbers together, and all the variables

(3r^2/2)-96=0

We get rid of parentheses

3r^2/2-96=0

We multiply all the terms by the denominator


3r^2-96*2=0

We add all the numbers together, and all the variables

3r^2-192=0

a = 3; b = 0; c = -192;
Δ = b2-4ac
Δ = 02-4·3·(-192)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*3}=\frac{-48}{6}
=-8
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*3}=\frac{48}{6}
=8
$