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2x^2-10x=22
We move all terms to the left:
2x^2-10x-(22)=0
a = 2; b = -10; c = -22;
Δ = b2-4ac
Δ = -102-4·2·(-22)
Δ = 276
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{69}}{2*2}=\frac{10-2\sqrt{69}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{69}}{2*2}=\frac{10+2\sqrt{69}}{4} $
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