a2-14a-39=7

Solution for a2-14a-39=7 equation:

a2-14a-39=7

We move all terms to the left:

a2-14a-39-(7)=0

We add all the numbers together, and all the variables

a^2-14a-46=0

a = 1; b = -14; c = -46;
Δ = b2-4ac
Δ = -142-4·1·(-46)
Δ = 380
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:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{95}}{2*1}=\frac{14-2\sqrt{95}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{95}}{2*1}=\frac{14+2\sqrt{95}}{2}
$