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10x(5x-2)=22
We move all terms to the left:
10x(5x-2)-(22)=0
We multiply parentheses
50x^2-20x-22=0
a = 50; b = -20; c = -22;
Δ = b2-4ac
Δ = -202-4·50·(-22)
Δ = 4800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-40\sqrt{3}}{2*50}=\frac{20-40\sqrt{3}}{100} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+40\sqrt{3}}{2*50}=\frac{20+40\sqrt{3}}{100} $
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