(4x-7)(9-x)=0

Solution for (4x-7)(9-x)=0 equation:

(4x-7)(9-x)=0

We add all the numbers together, and all the variables

(4x-7)(-1x+9)=0

We multiply parentheses ..

(-4x^2+36x+7x-63)=0

We get rid of parentheses

-4x^2+36x+7x-63=0

We add all the numbers together, and all the variables

-4x^2+43x-63=0

a = -4; b = 43; c = -63;
Δ = b2-4ac
Δ = 432-4·(-4)·(-63)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-29}{2*-4}=\frac{-72}{-8}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+29}{2*-4}=\frac{-14}{-8}
=1+3/4
$