3(x+5)3x+1=-32

Solution for 3(x+5)3x+1=-32 equation:

3(x+5)3x+1=-32

We move all terms to the left:

3(x+5)3x+1-(-32)=0

We add all the numbers together, and all the variables

3(x+5)3x+33=0

We multiply parentheses

9x^2+45x+33=0

a = 9; b = 45; c = +33;
Δ = b2-4ac
Δ = 452-4·9·33
Δ = 837
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:

$\sqrt{\Delta}=\sqrt{837}=\sqrt{9*93}=\sqrt{9}*\sqrt{93}=3\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{93}}{2*9}=\frac{-45-3\sqrt{93}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{93}}{2*9}=\frac{-45+3\sqrt{93}}{18}
$