(7x-2)(13-x)=0

Solution for (7x-2)(13-x)=0 equation:

(7x-2)(13-x)=0

We add all the numbers together, and all the variables

(7x-2)(-1x+13)=0

We multiply parentheses ..

(-7x^2+91x+2x-26)=0

We get rid of parentheses

-7x^2+91x+2x-26=0

We add all the numbers together, and all the variables

-7x^2+93x-26=0

a = -7; b = 93; c = -26;
Δ = b2-4ac
Δ = 932-4·(-7)·(-26)
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(93)-89}{2*-7}=\frac{-182}{-14}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+89}{2*-7}=\frac{-4}{-14}
=2/7
$