14=7x(8x+12)

Solution for 14=7x(8x+12) equation:

14=7x(8x+12)

We move all terms to the left:

14-(7x(8x+12))=0


We calculate terms in parentheses: -(7x(8x+12)), so:

7x(8x+12)

We multiply parentheses

56x^2+84x

Back to the equation:

-(56x^2+84x)


We get rid of parentheses

-56x^2-84x+14=0

a = -56; b = -84; c = +14;
Δ = b2-4ac
Δ = -842-4·(-56)·14
Δ = 10192
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:

$\sqrt{\Delta}=\sqrt{10192}=\sqrt{784*13}=\sqrt{784}*\sqrt{13}=28\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-28\sqrt{13}}{2*-56}=\frac{84-28\sqrt{13}}{-112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+28\sqrt{13}}{2*-56}=\frac{84+28\sqrt{13}}{-112}
$