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2x(5x-1)=22
We move all terms to the left:
2x(5x-1)-(22)=0
We multiply parentheses
10x^2-2x-22=0
a = 10; b = -2; c = -22;
Δ = b2-4ac
Δ = -22-4·10·(-22)
Δ = 884
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{884}=\sqrt{4*221}=\sqrt{4}*\sqrt{221}=2\sqrt{221}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{221}}{2*10}=\frac{2-2\sqrt{221}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{221}}{2*10}=\frac{2+2\sqrt{221}}{20} $
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