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3x(5x+3)=144
We move all terms to the left:
3x(5x+3)-(144)=0
We multiply parentheses
15x^2+9x-144=0
a = 15; b = 9; c = -144;
Δ = b2-4ac
Δ = 92-4·15·(-144)
Δ = 8721
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8721}=\sqrt{9*969}=\sqrt{9}*\sqrt{969}=3\sqrt{969}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{969}}{2*15}=\frac{-9-3\sqrt{969}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{969}}{2*15}=\frac{-9+3\sqrt{969}}{30} $
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