3r^2=42-5r

Solution for 3r^2=42-5r equation:

3r^2=42-5r

We move all terms to the left:

3r^2-(42-5r)=0

We add all the numbers together, and all the variables

3r^2-(-5r+42)=0

We get rid of parentheses

3r^2+5r-42=0

a = 3; b = 5; c = -42;
Δ = b2-4ac
Δ = 52-4·3·(-42)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-23}{2*3}=\frac{-28}{6}
=-4+2/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+23}{2*3}=\frac{18}{6}
=3
$