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8x^2+6x-5=22
We move all terms to the left:
8x^2+6x-5-(22)=0
We add all the numbers together, and all the variables
8x^2+6x-27=0
a = 8; b = 6; c = -27;
Δ = b2-4ac
Δ = 62-4·8·(-27)
Δ = 900
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{900}=30$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-30}{2*8}=\frac{-36}{16} =-2+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+30}{2*8}=\frac{24}{16} =1+1/2 $
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