(4x-7)(5-9x)=0

Solution for (4x-7)(5-9x)=0 equation:

(4x-7)(5-9x)=0

We add all the numbers together, and all the variables

(4x-7)(-9x+5)=0

We multiply parentheses ..

(-36x^2+20x+63x-35)=0

We get rid of parentheses

-36x^2+20x+63x-35=0

We add all the numbers together, and all the variables

-36x^2+83x-35=0

a = -36; b = 83; c = -35;
Δ = b2-4ac
Δ = 832-4·(-36)·(-35)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(83)-43}{2*-36}=\frac{-126}{-72}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(83)+43}{2*-36}=\frac{-40}{-72}
=5/9
$