16x+14(x+1)=30x(x+1)-16

Solution for 16x+14(x+1)=30x(x+1)-16 equation:

16x+14(x+1)=30x(x+1)-16

We move all terms to the left:

16x+14(x+1)-(30x(x+1)-16)=0

We multiply parentheses

16x+14x-(30x(x+1)-16)+14=0


We calculate terms in parentheses: -(30x(x+1)-16), so:

30x(x+1)-16

We multiply parentheses

30x^2+30x-16

Back to the equation:

-(30x^2+30x-16)


We add all the numbers together, and all the variables

30x-(30x^2+30x-16)+14=0

We get rid of parentheses

-30x^2+30x-30x+16+14=0

We add all the numbers together, and all the variables

-30x^2+30=0

a = -30; b = 0; c = +30;
Δ = b2-4ac
Δ = 02-4·(-30)·30
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60}{2*-30}=\frac{-60}{-60}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60}{2*-30}=\frac{60}{-60}
=-1
$