3x(x+7)=27

Solution for 3x(x+7)=27 equation:

3x(x+7)=27

We move all terms to the left:

3x(x+7)-(27)=0

We multiply parentheses

3x^2+21x-27=0

a = 3; b = 21; c = -27;
Δ = b2-4ac
Δ = 212-4·3·(-27)
Δ = 765
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:

$\sqrt{\Delta}=\sqrt{765}=\sqrt{9*85}=\sqrt{9}*\sqrt{85}=3\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{85}}{2*3}=\frac{-21-3\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{85}}{2*3}=\frac{-21+3\sqrt{85}}{6}
$