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5x(3x-1)=100
We move all terms to the left:
5x(3x-1)-(100)=0
We multiply parentheses
15x^2-5x-100=0
a = 15; b = -5; c = -100;
Δ = b2-4ac
Δ = -52-4·15·(-100)
Δ = 6025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6025}=\sqrt{25*241}=\sqrt{25}*\sqrt{241}=5\sqrt{241}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{241}}{2*15}=\frac{5-5\sqrt{241}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{241}}{2*15}=\frac{5+5\sqrt{241}}{30} $
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