x(x+3)=340

Solution for x(x+3)=340 equation:

x(x+3)=340

We move all terms to the left:

x(x+3)-(340)=0

We multiply parentheses

x^2+3x-340=0

a = 1; b = 3; c = -340;
Δ = b2-4ac
Δ = 32-4·1·(-340)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-37}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+37}{2*1}=\frac{34}{2}
=17
$