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(2x-5)x=50
We move all terms to the left:
(2x-5)x-(50)=0
We multiply parentheses
2x^2-5x-50=0
a = 2; b = -5; c = -50;
Δ = b2-4ac
Δ = -52-4·2·(-50)
Δ = 425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{17}}{2*2}=\frac{5-5\sqrt{17}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{17}}{2*2}=\frac{5+5\sqrt{17}}{4} $
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