(3x+5)(3x+5)+5(3x+5)+6=0

Solution for (3x+5)(3x+5)+5(3x+5)+6=0 equation:

(3x+5)(3x+5)+5(3x+5)+6=0

We multiply parentheses

(3x+5)(3x+5)+15x+25+6=0

We multiply parentheses ..

(+9x^2+15x+15x+25)+15x+25+6=0

We add all the numbers together, and all the variables

(+9x^2+15x+15x+25)+15x+31=0

We get rid of parentheses

9x^2+15x+15x+15x+25+31=0

We add all the numbers together, and all the variables

9x^2+45x+56=0

a = 9; b = 45; c = +56;
Δ = b2-4ac
Δ = 452-4·9·56
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3}{2*9}=\frac{-48}{18}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3}{2*9}=\frac{-42}{18}
=-2+1/3
$