(x+1)(10x)=x(12x+2)

Solution for (x+1)(10x)=x(12x+2) equation:

(x+1)(10x)=x(12x+2)

We move all terms to the left:

(x+1)(10x)-(x(12x+2))=0

We multiply parentheses

10x^2+10x-(x(12x+2))=0


We calculate terms in parentheses: -(x(12x+2)), so:

x(12x+2)

We multiply parentheses

12x^2+2x

Back to the equation:

-(12x^2+2x)


We get rid of parentheses

10x^2-12x^2+10x-2x=0

We add all the numbers together, and all the variables

-2x^2+8x=0

a = -2; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-2)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-2}=\frac{0}{-4}
=0
$