7x*12x=84*7

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Solution for 7x*12x=84*7 equation:



7x*12x=84*7
We move all terms to the left:
7x*12x-(84*7)=0
We add all the numbers together, and all the variables
7x*12x-588=0
Wy multiply elements
84x^2-588=0
a = 84; b = 0; c = -588;
Δ = b2-4ac
Δ = 02-4·84·(-588)
Δ = 197568
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:
$\sqrt{\Delta}=\sqrt{197568}=\sqrt{28224*7}=\sqrt{28224}*\sqrt{7}=168\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-168\sqrt{7}}{2*84}=\frac{0-168\sqrt{7}}{168} =-\frac{168\sqrt{7}}{168} =-\sqrt{7} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+168\sqrt{7}}{2*84}=\frac{0+168\sqrt{7}}{168} =\frac{168\sqrt{7}}{168} =\sqrt{7} $

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