3x(x-5)+2=11

Solution for 3x(x-5)+2=11 equation:

3x(x-5)+2=11

We move all terms to the left:

3x(x-5)+2-(11)=0

We add all the numbers together, and all the variables

3x(x-5)-9=0

We multiply parentheses

3x^2-15x-9=0

a = 3; b = -15; c = -9;
Δ = b2-4ac
Δ = -152-4·3·(-9)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{37}}{2*3}=\frac{15-3\sqrt{37}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{37}}{2*3}=\frac{15+3\sqrt{37}}{6}
$