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

Solution for 0=5x(3x+1)-7(3x+1) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(5x(3x+1)-7(3x+1)), so:

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

We multiply parentheses

15x^2+5x-21x-7

We add all the numbers together, and all the variables

15x^2-16x-7

Back to the equation:

-(15x^2-16x-7)


We get rid of parentheses

-15x^2+16x+7=0

a = -15; b = 16; c = +7;
Δ = b2-4ac
Δ = 162-4·(-15)·7
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-26}{2*-15}=\frac{-42}{-30}
=1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+26}{2*-15}=\frac{10}{-30}
=-1/3
$