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65(3x)(4x-39)=180
We move all terms to the left:
65(3x)(4x-39)-(180)=0
We multiply parentheses
2612x^2-25467x-180=0
a = 2612; b = -25467; c = -180;
Δ = b2-4ac
Δ = -254672-4·2612·(-180)
Δ = 650448729
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{650448729}=\sqrt{9*72272081}=\sqrt{9}*\sqrt{72272081}=3\sqrt{72272081}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25467)-3\sqrt{72272081}}{2*2612}=\frac{25467-3\sqrt{72272081}}{5224} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25467)+3\sqrt{72272081}}{2*2612}=\frac{25467+3\sqrt{72272081}}{5224} $
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