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15x^2+2x-2=22
We move all terms to the left:
15x^2+2x-2-(22)=0
We add all the numbers together, and all the variables
15x^2+2x-24=0
a = 15; b = 2; c = -24;
Δ = b2-4ac
Δ = 22-4·15·(-24)
Δ = 1444
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1444}=38$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-38}{2*15}=\frac{-40}{30} =-1+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+38}{2*15}=\frac{36}{30} =1+1/5 $
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