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5x^2-25x=125
We move all terms to the left:
5x^2-25x-(125)=0
a = 5; b = -25; c = -125;
Δ = b2-4ac
Δ = -252-4·5·(-125)
Δ = 3125
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3125}=\sqrt{625*5}=\sqrt{625}*\sqrt{5}=25\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25\sqrt{5}}{2*5}=\frac{25-25\sqrt{5}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25\sqrt{5}}{2*5}=\frac{25+25\sqrt{5}}{10} $
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