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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+15x^2-5x-9x+3)-((6x+1)(2x-5))=0


We calculate terms in parentheses: -((6x+1)(2x-5)), so:

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

We multiply parentheses ..

(+12x^2-30x+2x-5)

We get rid of parentheses

12x^2-30x+2x-5

We add all the numbers together, and all the variables

12x^2-28x-5

Back to the equation:

-(12x^2-28x-5)


We get rid of parentheses

15x^2-12x^2-5x-9x+28x+3+5=0

We add all the numbers together, and all the variables

3x^2+14x+8=0

a = 3; b = 14; c = +8;
Δ = b2-4ac
Δ = 142-4·3·8
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*3}=\frac{-4}{6}
=-2/3
$