(36-x)+x(28-x)=42

Solution for (36-x)+x(28-x)=42 equation:

(36-x)+x(28-x)=42

We move all terms to the left:

(36-x)+x(28-x)-(42)=0

We add all the numbers together, and all the variables

(-1x+36)+x(-1x+28)-42=0

We multiply parentheses

-1x^2+(-1x+36)+28x-42=0

We get rid of parentheses

-1x^2-1x+28x+36-42=0

We add all the numbers together, and all the variables

-1x^2+27x-6=0

a = -1; b = 27; c = -6;
Δ = b2-4ac
Δ = 272-4·(-1)·(-6)
Δ = 705
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{-(27)-\sqrt{705}}{2*-1}=\frac{-27-\sqrt{705}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{705}}{2*-1}=\frac{-27+\sqrt{705}}{-2}
$