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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

(+28x^2-36x-35x+45)+4x-5=0

We get rid of parentheses

28x^2-36x-35x+4x+45-5=0

We add all the numbers together, and all the variables

28x^2-67x+40=0

a = 28; b = -67; c = +40;
Δ = b2-4ac
Δ = -672-4·28·40
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-67)-3}{2*28}=\frac{64}{56}
=1+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67)+3}{2*28}=\frac{70}{56}
=1+1/4
$