7a^2-2a-38=0

Solution for 7a^2-2a-38=0 equation:

7a^2-2a-38=0

a = 7; b = -2; c = -38;
Δ = b2-4ac
Δ = -22-4·7·(-38)
Δ = 1068
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:

$\sqrt{\Delta}=\sqrt{1068}=\sqrt{4*267}=\sqrt{4}*\sqrt{267}=2\sqrt{267}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{267}}{2*7}=\frac{2-2\sqrt{267}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{267}}{2*7}=\frac{2+2\sqrt{267}}{14}
$