-8x-14=7(-2-4x)4x

Solution for -8x-14=7(-2-4x)4x equation:

-8x-14=7(-2-4x)4x

We move all terms to the left:

-8x-14-(7(-2-4x)4x)=0

We add all the numbers together, and all the variables

-8x-(7(-4x-2)4x)-14=0


We calculate terms in parentheses: -(7(-4x-2)4x), so:

7(-4x-2)4x

We multiply parentheses

-112x^2-56x

Back to the equation:

-(-112x^2-56x)


We get rid of parentheses

112x^2+56x-8x-14=0

We add all the numbers together, and all the variables

112x^2+48x-14=0

a = 112; b = 48; c = -14;
Δ = b2-4ac
Δ = 482-4·112·(-14)
Δ = 8576
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:

$\sqrt{\Delta}=\sqrt{8576}=\sqrt{64*134}=\sqrt{64}*\sqrt{134}=8\sqrt{134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{134}}{2*112}=\frac{-48-8\sqrt{134}}{224}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{134}}{2*112}=\frac{-48+8\sqrt{134}}{224}
$