3x(x+4)=10

Solution for 3x(x+4)=10 equation:

3x(x+4)=10

We move all terms to the left:

3x(x+4)-(10)=0

We multiply parentheses

3x^2+12x-10=0

a = 3; b = 12; c = -10;
Δ = b2-4ac
Δ = 122-4·3·(-10)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{66}}{2*3}=\frac{-12-2\sqrt{66}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{66}}{2*3}=\frac{-12+2\sqrt{66}}{6}
$