73=-6x(x-7)+6(x+6)

Solution for 73=-6x(x-7)+6(x+6) equation:

73=-6x(x-7)+6(x+6)

We move all terms to the left:

73-(-6x(x-7)+6(x+6))=0


We calculate terms in parentheses: -(-6x(x-7)+6(x+6)), so:

-6x(x-7)+6(x+6)

We multiply parentheses

-6x^2+42x+6x+36

We add all the numbers together, and all the variables

-6x^2+48x+36

Back to the equation:

-(-6x^2+48x+36)


We get rid of parentheses

6x^2-48x-36+73=0

We add all the numbers together, and all the variables

6x^2-48x+37=0

a = 6; b = -48; c = +37;
Δ = b2-4ac
Δ = -482-4·6·37
Δ = 1416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1416}=\sqrt{4*354}=\sqrt{4}*\sqrt{354}=2\sqrt{354}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{354}}{2*6}=\frac{48-2\sqrt{354}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{354}}{2*6}=\frac{48+2\sqrt{354}}{12}
$