(4x+7)(9-2x)=0

Solution for (4x+7)(9-2x)=0 equation:

(4x+7)(9-2x)=0

We add all the numbers together, and all the variables

(4x+7)(-2x+9)=0

We multiply parentheses ..

(-8x^2+36x-14x+63)=0

We get rid of parentheses

-8x^2+36x-14x+63=0

We add all the numbers together, and all the variables

-8x^2+22x+63=0

a = -8; b = 22; c = +63;
Δ = b2-4ac
Δ = 222-4·(-8)·63
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-50}{2*-8}=\frac{-72}{-16}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+50}{2*-8}=\frac{28}{-16}
=-1+3/4
$