(6x-1)(2-6x)=(3x-1)(2x+5)

Solution for (6x-1)(2-6x)=(3x-1)(2x+5) equation:

(6x-1)(2-6x)=(3x-1)(2x+5)

We move all terms to the left:

(6x-1)(2-6x)-((3x-1)(2x+5))=0

We add all the numbers together, and all the variables

(6x-1)(-6x+2)-((3x-1)(2x+5))=0

We multiply parentheses ..

(-36x^2+12x+6x-2)-((3x-1)(2x+5))=0


We calculate terms in parentheses: -((3x-1)(2x+5)), so:

(3x-1)(2x+5)

We multiply parentheses ..

(+6x^2+15x-2x-5)

We get rid of parentheses

6x^2+15x-2x-5

We add all the numbers together, and all the variables

6x^2+13x-5

Back to the equation:

-(6x^2+13x-5)


We get rid of parentheses

-36x^2-6x^2+12x+6x-13x-2+5=0

We add all the numbers together, and all the variables

-42x^2+5x+3=0

a = -42; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-42)·3
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-23}{2*-42}=\frac{-28}{-84}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+23}{2*-42}=\frac{18}{-84}
=-3/14
$