(2w+13)(w-5)=0

Solution for (2w+13)(w-5)=0 equation:

(2w+13)(w-5)=0

We multiply parentheses ..

(+2w^2-10w+13w-65)=0

We get rid of parentheses

2w^2-10w+13w-65=0

We add all the numbers together, and all the variables

2w^2+3w-65=0

a = 2; b = 3; c = -65;
Δ = b2-4ac
Δ = 32-4·2·(-65)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-23}{2*2}=\frac{-26}{4}
=-6+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+23}{2*2}=\frac{20}{4}
=5
$