3x(x-16)=51

Solution for 3x(x-16)=51 equation:

3x(x-16)=51

We move all terms to the left:

3x(x-16)-(51)=0

We multiply parentheses

3x^2-48x-51=0

a = 3; b = -48; c = -51;
Δ = b2-4ac
Δ = -482-4·3·(-51)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-54}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+54}{2*3}=\frac{102}{6}
=17
$