3x(x+11)+5=68

Solution for 3x(x+11)+5=68 equation:

3x(x+11)+5=68

We move all terms to the left:

3x(x+11)+5-(68)=0

We add all the numbers together, and all the variables

3x(x+11)-63=0

We multiply parentheses

3x^2+33x-63=0

a = 3; b = 33; c = -63;
Δ = b2-4ac
Δ = 332-4·3·(-63)
Δ = 1845
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1845}=\sqrt{9*205}=\sqrt{9}*\sqrt{205}=3\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{205}}{2*3}=\frac{-33-3\sqrt{205}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{205}}{2*3}=\frac{-33+3\sqrt{205}}{6}
$