3x(x+6)+10=0

Solution for 3x(x+6)+10=0 equation:

3x(x+6)+10=0

We multiply parentheses

3x^2+18x+10=0

a = 3; b = 18; c = +10;
Δ = b2-4ac
Δ = 182-4·3·10
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{51}}{2*3}=\frac{-18-2\sqrt{51}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{51}}{2*3}=\frac{-18+2\sqrt{51}}{6}
$