(2x+11)(5-x)=55

Solution for (2x+11)(5-x)=55 equation:

(2x+11)(5-x)=55

We move all terms to the left:

(2x+11)(5-x)-(55)=0

We add all the numbers together, and all the variables

(2x+11)(-1x+5)-55=0

We multiply parentheses ..

(-2x^2+10x-11x+55)-55=0

We get rid of parentheses

-2x^2+10x-11x+55-55=0

We add all the numbers together, and all the variables

-2x^2-1x=0

a = -2; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-2)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-2}=\frac{2}{-4}
=-1/2
$