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3x(5x-4)=180
We move all terms to the left:
3x(5x-4)-(180)=0
We multiply parentheses
15x^2-12x-180=0
a = 15; b = -12; c = -180;
Δ = b2-4ac
Δ = -122-4·15·(-180)
Δ = 10944
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10944}=\sqrt{576*19}=\sqrt{576}*\sqrt{19}=24\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24\sqrt{19}}{2*15}=\frac{12-24\sqrt{19}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24\sqrt{19}}{2*15}=\frac{12+24\sqrt{19}}{30} $
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