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225x^2-1=6
We move all terms to the left:
225x^2-1-(6)=0
We add all the numbers together, and all the variables
225x^2-7=0
a = 225; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·225·(-7)
Δ = 6300
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6300}=\sqrt{900*7}=\sqrt{900}*\sqrt{7}=30\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{7}}{2*225}=\frac{0-30\sqrt{7}}{450} =-\frac{30\sqrt{7}}{450} =-\frac{\sqrt{7}}{15} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{7}}{2*225}=\frac{0+30\sqrt{7}}{450} =\frac{30\sqrt{7}}{450} =\frac{\sqrt{7}}{15} $
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