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4x^2-9x-1=7
We move all terms to the left:
4x^2-9x-1-(7)=0
We add all the numbers together, and all the variables
4x^2-9x-8=0
a = 4; b = -9; c = -8;
Δ = b2-4ac
Δ = -92-4·4·(-8)
Δ = 209
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{209}}{2*4}=\frac{9-\sqrt{209}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{209}}{2*4}=\frac{9+\sqrt{209}}{8} $
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