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5x(5x-1)=120
We move all terms to the left:
5x(5x-1)-(120)=0
We multiply parentheses
25x^2-5x-120=0
a = 25; b = -5; c = -120;
Δ = b2-4ac
Δ = -52-4·25·(-120)
Δ = 12025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12025}=\sqrt{25*481}=\sqrt{25}*\sqrt{481}=5\sqrt{481}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{481}}{2*25}=\frac{5-5\sqrt{481}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{481}}{2*25}=\frac{5+5\sqrt{481}}{50} $
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