2a(3+5a)=22

Solution for 2a(3+5a)=22 equation:

2a(3+5a)=22

We move all terms to the left:

2a(3+5a)-(22)=0

We add all the numbers together, and all the variables

2a(5a+3)-22=0

We multiply parentheses

10a^2+6a-22=0

a = 10; b = 6; c = -22;
Δ = b2-4ac
Δ = 62-4·10·(-22)
Δ = 916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{229}}{2*10}=\frac{-6-2\sqrt{229}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{229}}{2*10}=\frac{-6+2\sqrt{229}}{20}
$