78=7x+x(x+12)

Solution for 78=7x+x(x+12) equation:

78=7x+x(x+12)

We move all terms to the left:

78-(7x+x(x+12))=0


We calculate terms in parentheses: -(7x+x(x+12)), so:

7x+x(x+12)

We multiply parentheses

x^2+7x+12x

We add all the numbers together, and all the variables

x^2+19x

Back to the equation:

-(x^2+19x)


We get rid of parentheses

-x^2-19x+78=0

We add all the numbers together, and all the variables

-1x^2-19x+78=0

a = -1; b = -19; c = +78;
Δ = b2-4ac
Δ = -192-4·(-1)·78
Δ = 673
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{673}}{2*-1}=\frac{19-\sqrt{673}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{673}}{2*-1}=\frac{19+\sqrt{673}}{-2}
$