(x+3)(5x-1)=(x+3)(2x-7)

Solution for (x+3)(5x-1)=(x+3)(2x-7) equation:

(x+3)(5x-1)=(x+3)(2x-7)

We move all terms to the left:

(x+3)(5x-1)-((x+3)(2x-7))=0

We multiply parentheses ..

(+5x^2-1x+15x-3)-((x+3)(2x-7))=0


We calculate terms in parentheses: -((x+3)(2x-7)), so:

(x+3)(2x-7)

We multiply parentheses ..

(+2x^2-7x+6x-21)

We get rid of parentheses

2x^2-7x+6x-21

We add all the numbers together, and all the variables

2x^2-1x-21

Back to the equation:

-(2x^2-1x-21)


We get rid of parentheses

5x^2-2x^2-1x+15x+1x-3+21=0

We add all the numbers together, and all the variables

3x^2+15x+18=0

a = 3; b = 15; c = +18;
Δ = b2-4ac
Δ = 152-4·3·18
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3}{2*3}=\frac{-12}{6}
=-2
$