3+x(5+x)=35

Solution for 3+x(5+x)=35 equation:

3+x(5+x)=35

We move all terms to the left:

3+x(5+x)-(35)=0

We add all the numbers together, and all the variables

x(x+5)+3-35=0

We add all the numbers together, and all the variables

x(x+5)-32=0

We multiply parentheses

x^2+5x-32=0

a = 1; b = 5; c = -32;
Δ = b2-4ac
Δ = 52-4·1·(-32)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{17}}{2*1}=\frac{-5-3\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{17}}{2*1}=\frac{-5+3\sqrt{17}}{2}
$