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9x(4x-15)=38
We move all terms to the left:
9x(4x-15)-(38)=0
We multiply parentheses
36x^2-135x-38=0
a = 36; b = -135; c = -38;
Δ = b2-4ac
Δ = -1352-4·36·(-38)
Δ = 23697
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{23697}=\sqrt{9*2633}=\sqrt{9}*\sqrt{2633}=3\sqrt{2633}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-3\sqrt{2633}}{2*36}=\frac{135-3\sqrt{2633}}{72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+3\sqrt{2633}}{2*36}=\frac{135+3\sqrt{2633}}{72} $
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