14-2(x+8)=5x(-3x-34)

Solution for 14-2(x+8)=5x(-3x-34) equation:

14-2(x+8)=5x(-3x-34)

We move all terms to the left:

14-2(x+8)-(5x(-3x-34))=0

We multiply parentheses

-2x-(5x(-3x-34))-16+14=0


We calculate terms in parentheses: -(5x(-3x-34)), so:

5x(-3x-34)

We multiply parentheses

-15x^2-170x

Back to the equation:

-(-15x^2-170x)


We add all the numbers together, and all the variables

-(-15x^2-170x)-2x-2=0

We get rid of parentheses

15x^2+170x-2x-2=0

We add all the numbers together, and all the variables

15x^2+168x-2=0

a = 15; b = 168; c = -2;
Δ = b2-4ac
Δ = 1682-4·15·(-2)
Δ = 28344
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:

$\sqrt{\Delta}=\sqrt{28344}=\sqrt{4*7086}=\sqrt{4}*\sqrt{7086}=2\sqrt{7086}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-2\sqrt{7086}}{2*15}=\frac{-168-2\sqrt{7086}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+2\sqrt{7086}}{2*15}=\frac{-168+2\sqrt{7086}}{30}
$