2a(a+7)=38

Solution for 2a(a+7)=38 equation:

2a(a+7)=38

We move all terms to the left:

2a(a+7)-(38)=0

We multiply parentheses

2a^2+14a-38=0

a = 2; b = 14; c = -38;
Δ = b2-4ac
Δ = 142-4·2·(-38)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10\sqrt{5}}{2*2}=\frac{-14-10\sqrt{5}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10\sqrt{5}}{2*2}=\frac{-14+10\sqrt{5}}{4}
$