9x(3x+5)=42

Solution for 9x(3x+5)=42 equation:

9x(3x+5)=42

We move all terms to the left:

9x(3x+5)-(42)=0

We multiply parentheses

27x^2+45x-42=0

a = 27; b = 45; c = -42;
Δ = b2-4ac
Δ = 452-4·27·(-42)
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-81}{2*27}=\frac{-126}{54}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+81}{2*27}=\frac{36}{54}
=2/3
$