x(x+3)=+34=(x+5)x+2)

Solution for x(x+3)=+34=(x+5)x+2) equation:

x(x+3)=+34=(x+5)x+2)

We move all terms to the left:

x(x+3)-(+34)=0

We add all the numbers together, and all the variables

x(x+3)-34=0

We multiply parentheses

x^2+3x-34=0

a = 1; b = 3; c = -34;
Δ = b2-4ac
Δ = 32-4·1·(-34)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{145}}{2*1}=\frac{-3-\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{145}}{2*1}=\frac{-3+\sqrt{145}}{2}
$