(4x-3)(5x-3)=(8x-7)(3x-1)

Solution for (4x-3)(5x-3)=(8x-7)(3x-1) equation:

(4x-3)(5x-3)=(8x-7)(3x-1)

We move all terms to the left:

(4x-3)(5x-3)-((8x-7)(3x-1))=0

We multiply parentheses ..

(+20x^2-12x-15x+9)-((8x-7)(3x-1))=0


We calculate terms in parentheses: -((8x-7)(3x-1)), so:

(8x-7)(3x-1)

We multiply parentheses ..

(+24x^2-8x-21x+7)

We get rid of parentheses

24x^2-8x-21x+7

We add all the numbers together, and all the variables

24x^2-29x+7

Back to the equation:

-(24x^2-29x+7)


We get rid of parentheses

20x^2-24x^2-12x-15x+29x+9-7=0

We add all the numbers together, and all the variables

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

a = -4; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-4)·2
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*-4}=\frac{4}{-8}
=-1/2
$