(x+5)(3x+5)=66

Solution for (x+5)(3x+5)=66 equation:

(x+5)(3x+5)=66

We move all terms to the left:

(x+5)(3x+5)-(66)=0

We multiply parentheses ..

(+3x^2+5x+15x+25)-66=0

We get rid of parentheses

3x^2+5x+15x+25-66=0

We add all the numbers together, and all the variables

3x^2+20x-41=0

a = 3; b = 20; c = -41;
Δ = b2-4ac
Δ = 202-4·3·(-41)
Δ = 892
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:

$\sqrt{\Delta}=\sqrt{892}=\sqrt{4*223}=\sqrt{4}*\sqrt{223}=2\sqrt{223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{223}}{2*3}=\frac{-20-2\sqrt{223}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{223}}{2*3}=\frac{-20+2\sqrt{223}}{6}
$