x(x+5)+3(x+5)=65

Solution for x(x+5)+3(x+5)=65 equation:

x(x+5)+3(x+5)=65

We move all terms to the left:

x(x+5)+3(x+5)-(65)=0

We multiply parentheses

x^2+5x+3x+15-65=0

We add all the numbers together, and all the variables

x^2+8x-50=0

a = 1; b = 8; c = -50;
Δ = b2-4ac
Δ = 82-4·1·(-50)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{66}}{2*1}=\frac{-8-2\sqrt{66}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{66}}{2*1}=\frac{-8+2\sqrt{66}}{2}
$