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144=9x^2/7
We move all terms to the left:
144-(9x^2/7)=0
We get rid of parentheses
-9x^2/7+144=0
We multiply all the terms by the denominator
-9x^2+144*7=0
We add all the numbers together, and all the variables
-9x^2+1008=0
a = -9; b = 0; c = +1008;
Δ = b2-4ac
Δ = 02-4·(-9)·1008
Δ = 36288
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{36288}=\sqrt{5184*7}=\sqrt{5184}*\sqrt{7}=72\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{7}}{2*-9}=\frac{0-72\sqrt{7}}{-18} =-\frac{72\sqrt{7}}{-18} =-\frac{4\sqrt{7}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{7}}{2*-9}=\frac{0+72\sqrt{7}}{-18} =\frac{72\sqrt{7}}{-18} =\frac{4\sqrt{7}}{-1} $
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