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5x(6x-8)=180
We move all terms to the left:
5x(6x-8)-(180)=0
We multiply parentheses
30x^2-40x-180=0
a = 30; b = -40; c = -180;
Δ = b2-4ac
Δ = -402-4·30·(-180)
Δ = 23200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{23200}=\sqrt{400*58}=\sqrt{400}*\sqrt{58}=20\sqrt{58}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20\sqrt{58}}{2*30}=\frac{40-20\sqrt{58}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20\sqrt{58}}{2*30}=\frac{40+20\sqrt{58}}{60} $
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