3x(x+5)=42

Solution for 3x(x+5)=42 equation:

3x(x+5)=42

We move all terms to the left:

3x(x+5)-(42)=0

We multiply parentheses

3x^2+15x-42=0

a = 3; b = 15; c = -42;
Δ = b2-4ac
Δ = 152-4·3·(-42)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-27}{2*3}=\frac{-42}{6}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+27}{2*3}=\frac{12}{6}
=2
$