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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+24x^2-8x-21x+7)-((4x-3)(5x-3))=0


We calculate terms in parentheses: -((4x-3)(5x-3)), so:

(4x-3)(5x-3)

We multiply parentheses ..

(+20x^2-12x-15x+9)

We get rid of parentheses

20x^2-12x-15x+9

We add all the numbers together, and all the variables

20x^2-27x+9

Back to the equation:

-(20x^2-27x+9)


We get rid of parentheses

24x^2-20x^2-8x-21x+27x+7-9=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{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*4}=\frac{8}{8}
=1
$