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15x^2=4/9
We move all terms to the left:
15x^2-(4/9)=0
We add all the numbers together, and all the variables
15x^2-(+4/9)=0
We get rid of parentheses
15x^2-4/9=0
We multiply all the terms by the denominator
15x^2*9-4=0
Wy multiply elements
135x^2-4=0
a = 135; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·135·(-4)
Δ = 2160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{15}}{2*135}=\frac{0-12\sqrt{15}}{270} =-\frac{12\sqrt{15}}{270} =-\frac{2\sqrt{15}}{45} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{15}}{2*135}=\frac{0+12\sqrt{15}}{270} =\frac{12\sqrt{15}}{270} =\frac{2\sqrt{15}}{45} $
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