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9x^2-10=170
We move all terms to the left:
9x^2-10-(170)=0
We add all the numbers together, and all the variables
9x^2-180=0
a = 9; b = 0; c = -180;
Δ = b2-4ac
Δ = 02-4·9·(-180)
Δ = 6480
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{5}}{2*9}=\frac{0-36\sqrt{5}}{18} =-\frac{36\sqrt{5}}{18} =-2\sqrt{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{5}}{2*9}=\frac{0+36\sqrt{5}}{18} =\frac{36\sqrt{5}}{18} =2\sqrt{5} $
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