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x=7+x+6(-3/7)
We move all terms to the left:
x-(7+x+6(-3/7))=0
We multiply all the terms by the denominator
x*7))-(7+x+6(-3=0
Wy multiply elements
7x^2-3=0
a = 7; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·7·(-3)
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*7}=\frac{0-2\sqrt{21}}{14} =-\frac{2\sqrt{21}}{14} =-\frac{\sqrt{21}}{7} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*7}=\frac{0+2\sqrt{21}}{14} =\frac{2\sqrt{21}}{14} =\frac{\sqrt{21}}{7} $
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