x^2+5.4x^2=7000

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Solution for x^2+5.4x^2=7000 equation:



x^2+5.4x^2=7000
We move all terms to the left:
x^2+5.4x^2-(7000)=0
We add all the numbers together, and all the variables
6.4x^2-7000=0
a = 6.4; b = 0; c = -7000;
Δ = b2-4ac
Δ = 02-4·6.4·(-7000)
Δ = 179200
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:
$\sqrt{\Delta}=\sqrt{179200}=\sqrt{25600*7}=\sqrt{25600}*\sqrt{7}=160\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-160\sqrt{7}}{2*6.4}=\frac{0-160\sqrt{7}}{12.8} =-\frac{160\sqrt{7}}{12.8} =-\frac{40\sqrt{7}}{3.2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+160\sqrt{7}}{2*6.4}=\frac{0+160\sqrt{7}}{12.8} =\frac{160\sqrt{7}}{12.8} =\frac{40\sqrt{7}}{3.2} $

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