7x2-15=45

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Solution for 7x2-15=45 equation:



7x^2-15=45
We move all terms to the left:
7x^2-15-(45)=0
We add all the numbers together, and all the variables
7x^2-60=0
a = 7; b = 0; c = -60;
Δ = b2-4ac
Δ = 02-4·7·(-60)
Δ = 1680
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:
$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*7}=\frac{0-4\sqrt{105}}{14} =-\frac{4\sqrt{105}}{14} =-\frac{2\sqrt{105}}{7} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*7}=\frac{0+4\sqrt{105}}{14} =\frac{4\sqrt{105}}{14} =\frac{2\sqrt{105}}{7} $

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