3x(4-5x)=(2x-3)(5x-4)

Solution for 3x(4-5x)=(2x-3)(5x-4) equation:

3x(4-5x)=(2x-3)(5x-4)

We move all terms to the left:

3x(4-5x)-((2x-3)(5x-4))=0

We add all the numbers together, and all the variables

3x(-5x+4)-((2x-3)(5x-4))=0

We multiply parentheses

-15x^2+12x-((2x-3)(5x-4))=0

We multiply parentheses ..

-15x^2-((+10x^2-8x-15x+12))+12x=0


We calculate terms in parentheses: -((+10x^2-8x-15x+12)), so:

(+10x^2-8x-15x+12)

We get rid of parentheses

10x^2-8x-15x+12

We add all the numbers together, and all the variables

10x^2-23x+12

Back to the equation:

-(10x^2-23x+12)


We add all the numbers together, and all the variables

-15x^2+12x-(10x^2-23x+12)=0

We get rid of parentheses

-15x^2-10x^2+12x+23x-12=0

We add all the numbers together, and all the variables

-25x^2+35x-12=0

a = -25; b = 35; c = -12;
Δ = b2-4ac
Δ = 352-4·(-25)·(-12)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-5}{2*-25}=\frac{-40}{-50}
=4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+5}{2*-25}=\frac{-30}{-50}
=3/5
$