(4x+6)3+14=4*(5-2x)4x

Solution for (4x+6)3+14=4*(5-2x)4x equation:

(4x+6)3+14=4(5-2x)4x

We move all terms to the left:

(4x+6)3+14-(4(5-2x)4x)=0

We add all the numbers together, and all the variables

(4x+6)3-(4(-2x+5)4x)+14=0

We multiply parentheses

12x-(4(-2x+5)4x)+18+14=0


We calculate terms in parentheses: -(4(-2x+5)4x), so:

4(-2x+5)4x

We multiply parentheses

-32x^2+80x

Back to the equation:

-(-32x^2+80x)


We add all the numbers together, and all the variables

-(-32x^2+80x)+12x+32=0

We get rid of parentheses

32x^2-80x+12x+32=0

We add all the numbers together, and all the variables

32x^2-68x+32=0

a = 32; b = -68; c = +32;
Δ = b2-4ac
Δ = -682-4·32·32
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{33}}{2*32}=\frac{68-4\sqrt{33}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{33}}{2*32}=\frac{68+4\sqrt{33}}{64}
$