14x(28x+14x)=-21(42x-21)

Solution for 14x(28x+14x)=-21(42x-21) equation:

14x(28x+14x)=-21(42x-21)

We move all terms to the left:

14x(28x+14x)-(-21(42x-21))=0

We add all the numbers together, and all the variables

14x(+42x)-(-21(42x-21))=0

We multiply parentheses

588x^2-(-21(42x-21))=0


We calculate terms in parentheses: -(-21(42x-21)), so:

-21(42x-21)

We multiply parentheses

-882x+441

Back to the equation:

-(-882x+441)


We get rid of parentheses

588x^2+882x-441=0

a = 588; b = 882; c = -441;
Δ = b2-4ac
Δ = 8822-4·588·(-441)
Δ = 1815156
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:

$\sqrt{\Delta}=\sqrt{1815156}=\sqrt{86436*21}=\sqrt{86436}*\sqrt{21}=294\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(882)-294\sqrt{21}}{2*588}=\frac{-882-294\sqrt{21}}{1176}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(882)+294\sqrt{21}}{2*588}=\frac{-882+294\sqrt{21}}{1176}
$