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2x^2-9x-7=7
We move all terms to the left:
2x^2-9x-7-(7)=0
We add all the numbers together, and all the variables
2x^2-9x-14=0
a = 2; b = -9; c = -14;
Δ = b2-4ac
Δ = -92-4·2·(-14)
Δ = 193
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{193}}{2*2}=\frac{9-\sqrt{193}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{193}}{2*2}=\frac{9+\sqrt{193}}{4} $
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