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9x(2x-7)=15
We move all terms to the left:
9x(2x-7)-(15)=0
We multiply parentheses
18x^2-63x-15=0
a = 18; b = -63; c = -15;
Δ = b2-4ac
Δ = -632-4·18·(-15)
Δ = 5049
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5049}=\sqrt{9*561}=\sqrt{9}*\sqrt{561}=3\sqrt{561}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{561}}{2*18}=\frac{63-3\sqrt{561}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{561}}{2*18}=\frac{63+3\sqrt{561}}{36} $
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