3r2=14r-8

Solution for 3r2=14r-8 equation:

3r^2=14r-8

We move all terms to the left:

3r^2-(14r-8)=0

We get rid of parentheses

3r^2-14r+8=0

a = 3; b = -14; c = +8;
Δ = b2-4ac
Δ = -142-4·3·8
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10}{2*3}=\frac{4}{6}
=2/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*3}=\frac{24}{6}
=4
$