(4x-5)(3x-7)=3

Solution for (4x-5)(3x-7)=3 equation:

(4x-5)(3x-7)=3

We move all terms to the left:

(4x-5)(3x-7)-(3)=0

We multiply parentheses ..

(+12x^2-28x-15x+35)-3=0

We get rid of parentheses

12x^2-28x-15x+35-3=0

We add all the numbers together, and all the variables

12x^2-43x+32=0

a = 12; b = -43; c = +32;
Δ = b2-4ac
Δ = -432-4·12·32
Δ = 313
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-\sqrt{313}}{2*12}=\frac{43-\sqrt{313}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+\sqrt{313}}{2*12}=\frac{43+\sqrt{313}}{24}
$