(-27-2x)(13-x)=0

Solution for (-27-2x)(13-x)=0 equation:

(-27-2x)(13-x)=0

We add all the numbers together, and all the variables

(-2x-27)(-1x+13)=0

We multiply parentheses ..

(+2x^2-26x+27x-351)=0

We get rid of parentheses

2x^2-26x+27x-351=0

We add all the numbers together, and all the variables

2x^2+x-351=0

a = 2; b = 1; c = -351;
Δ = b2-4ac
Δ = 12-4·2·(-351)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-53}{2*2}=\frac{-54}{4}
=-13+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+53}{2*2}=\frac{52}{4}
=13
$