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32x^2-5x-3=1
We move all terms to the left:
32x^2-5x-3-(1)=0
We add all the numbers together, and all the variables
32x^2-5x-4=0
a = 32; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·32·(-4)
Δ = 537
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{-(-5)-\sqrt{537}}{2*32}=\frac{5-\sqrt{537}}{64} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{537}}{2*32}=\frac{5+\sqrt{537}}{64} $
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