(7+x)x=78

Solution for (7+x)x=78 equation:

(7+x)x=78

We move all terms to the left:

(7+x)x-(78)=0

We add all the numbers together, and all the variables

(x+7)x-78=0

We multiply parentheses

x^2+7x-78=0

a = 1; b = 7; c = -78;
Δ = b2-4ac
Δ = 72-4·1·(-78)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-19}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+19}{2*1}=\frac{12}{2}
=6
$