78=x(x+7)

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

78=x(x+7)

We move all terms to the left:

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


We calculate terms in parentheses: -(x(x+7)), so:

x(x+7)

We multiply parentheses

x^2+7x

Back to the equation:

-(x^2+7x)


We get rid of parentheses

-x^2-7x+78=0

We add all the numbers together, and all the variables

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