15(x+1)(x+1)=16(x+1)

Solution for 15(x+1)(x+1)=16(x+1) equation:

15(x+1)(x+1)=16(x+1)

We move all terms to the left:

15(x+1)(x+1)-(16(x+1))=0

We multiply parentheses ..

15(+x^2+x+x+1)-(16(x+1))=0


We calculate terms in parentheses: -(16(x+1)), so:

16(x+1)

We multiply parentheses

16x+16

Back to the equation:

-(16x+16)


We multiply parentheses

15x^2+15x+15x-(16x+16)+15=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

15x^2+14x-1=0

a = 15; b = 14; c = -1;
Δ = b2-4ac
Δ = 142-4·15·(-1)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-16}{2*15}=\frac{-30}{30}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+16}{2*15}=\frac{2}{30}
=1/15
$