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

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

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

We move all terms to the left:

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

We multiply parentheses

3x^2-15x-(3x-11)+3=0

We get rid of parentheses

3x^2-15x-3x+11+3=0

We add all the numbers together, and all the variables

3x^2-18x+14=0

a = 3; b = -18; c = +14;
Δ = b2-4ac
Δ = -182-4·3·14
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{39}}{2*3}=\frac{18-2\sqrt{39}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{39}}{2*3}=\frac{18+2\sqrt{39}}{6}
$