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15(x+2)9x=6
We move all terms to the left:
15(x+2)9x-(6)=0
We multiply parentheses
135x^2+270x-6=0
a = 135; b = 270; c = -6;
Δ = b2-4ac
Δ = 2702-4·135·(-6)
Δ = 76140
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{76140}=\sqrt{324*235}=\sqrt{324}*\sqrt{235}=18\sqrt{235}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-18\sqrt{235}}{2*135}=\frac{-270-18\sqrt{235}}{270} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+18\sqrt{235}}{2*135}=\frac{-270+18\sqrt{235}}{270} $
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