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

Solution for (2x-11)(x+5)=0 equation:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-1x-55=0

a = 2; b = -1; c = -55;
Δ = b2-4ac
Δ = -12-4·2·(-55)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-21}{2*2}=\frac{-20}{4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+21}{2*2}=\frac{22}{4}
=5+1/2
$