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8x^2-14x=9
We move all terms to the left:
8x^2-14x-(9)=0
a = 8; b = -14; c = -9;
Δ = b2-4ac
Δ = -142-4·8·(-9)
Δ = 484
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{484}=22$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-22}{2*8}=\frac{-8}{16} =-1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+22}{2*8}=\frac{36}{16} =2+1/4 $
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