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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

7(x+1)

We multiply parentheses

7x+7

Back to the equation:

-(7x+7)


We get rid of parentheses

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

We add all the numbers together, and all the variables

15x^2-22x-7=0

a = 15; b = -22; c = -7;
Δ = b2-4ac
Δ = -222-4·15·(-7)
Δ = 904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{226}}{2*15}=\frac{22-2\sqrt{226}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{226}}{2*15}=\frac{22+2\sqrt{226}}{30}
$