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3x(5x+30)=27
We move all terms to the left:
3x(5x+30)-(27)=0
We multiply parentheses
15x^2+90x-27=0
a = 15; b = 90; c = -27;
Δ = b2-4ac
Δ = 902-4·15·(-27)
Δ = 9720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9720}=\sqrt{324*30}=\sqrt{324}*\sqrt{30}=18\sqrt{30}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-18\sqrt{30}}{2*15}=\frac{-90-18\sqrt{30}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+18\sqrt{30}}{2*15}=\frac{-90+18\sqrt{30}}{30} $
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