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17=4x^2-3x+5
We move all terms to the left:
17-(4x^2-3x+5)=0
We get rid of parentheses
-4x^2+3x-5+17=0
We add all the numbers together, and all the variables
-4x^2+3x+12=0
a = -4; b = 3; c = +12;
Δ = b2-4ac
Δ = 32-4·(-4)·12
Δ = 201
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{-(3)-\sqrt{201}}{2*-4}=\frac{-3-\sqrt{201}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{201}}{2*-4}=\frac{-3+\sqrt{201}}{-8} $
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