3r^2-11r=42

Solution for 3r^2-11r=42 equation:

3r^2-11r=42

We move all terms to the left:

3r^2-11r-(42)=0

a = 3; b = -11; c = -42;
Δ = b2-4ac
Δ = -112-4·3·(-42)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-25}{2*3}=\frac{-14}{6}
=-2+1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+25}{2*3}=\frac{36}{6}
=6
$