(5x-7)(9-x)=0

Solution for (5x-7)(9-x)=0 equation:

(5x-7)(9-x)=0

We add all the numbers together, and all the variables

(5x-7)(-1x+9)=0

We multiply parentheses ..

(-5x^2+45x+7x-63)=0

We get rid of parentheses

-5x^2+45x+7x-63=0

We add all the numbers together, and all the variables

-5x^2+52x-63=0

a = -5; b = 52; c = -63;
Δ = b2-4ac
Δ = 522-4·(-5)·(-63)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-38}{2*-5}=\frac{-90}{-10}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+38}{2*-5}=\frac{-14}{-10}
=1+2/5
$