78=(x+6)(x-3)

Solution for 78=(x+6)(x-3) equation:

78=(x+6)(x-3)

We move all terms to the left:

78-((x+6)(x-3))=0

We multiply parentheses ..

-((+x^2-3x+6x-18))+78=0


We calculate terms in parentheses: -((+x^2-3x+6x-18)), so:

(+x^2-3x+6x-18)

We get rid of parentheses

x^2-3x+6x-18

We add all the numbers together, and all the variables

x^2+3x-18

Back to the equation:

-(x^2+3x-18)


We get rid of parentheses

-x^2-3x+18+78=0

We add all the numbers together, and all the variables

-1x^2-3x+96=0

a = -1; b = -3; c = +96;
Δ = b2-4ac
Δ = -32-4·(-1)·96
Δ = 393
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{-(-3)-\sqrt{393}}{2*-1}=\frac{3-\sqrt{393}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{393}}{2*-1}=\frac{3+\sqrt{393}}{-2}
$