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5x^2-24x+22=0
a = 5; b = -24; c = +22;
Δ = b2-4ac
Δ = -242-4·5·22
Δ = 136
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{34}}{2*5}=\frac{24-2\sqrt{34}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{34}}{2*5}=\frac{24+2\sqrt{34}}{10} $
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