a(3a+5)=42

Solution for a(3a+5)=42 equation:

a(3a+5)=42

We move all terms to the left:

a(3a+5)-(42)=0

We multiply parentheses

3a^2+5a-42=0

a = 3; b = 5; c = -42;
Δ = b2-4ac
Δ = 52-4·3·(-42)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-23}{2*3}=\frac{-28}{6}
=-4+2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+23}{2*3}=\frac{18}{6}
=3
$