340=a(a+3)

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

340=a(a+3)

We move all terms to the left:

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


We calculate terms in parentheses: -(a(a+3)), so:

a(a+3)

We multiply parentheses

a^2+3a

Back to the equation:

-(a^2+3a)


We get rid of parentheses

-a^2-3a+340=0

We add all the numbers together, and all the variables

-1a^2-3a+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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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