7a^2=78+14a

Solution for 7a^2=78+14a equation:

7a^2=78+14a

We move all terms to the left:

7a^2-(78+14a)=0

We add all the numbers together, and all the variables

7a^2-(14a+78)=0

We get rid of parentheses

7a^2-14a-78=0

a = 7; b = -14; c = -78;
Δ = b2-4ac
Δ = -142-4·7·(-78)
Δ = 2380
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:

$\sqrt{\Delta}=\sqrt{2380}=\sqrt{4*595}=\sqrt{4}*\sqrt{595}=2\sqrt{595}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{595}}{2*7}=\frac{14-2\sqrt{595}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{595}}{2*7}=\frac{14+2\sqrt{595}}{14}
$