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3x-x^2+11/4=0
We add all the numbers together, and all the variables
-1x^2+3x+11/4=0
We multiply all the terms by the denominator
-1x^2*4+3x*4+11=0
Wy multiply elements
-4x^2+12x+11=0
a = -4; b = 12; c = +11;
Δ = b2-4ac
Δ = 122-4·(-4)·11
Δ = 320
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{5}}{2*-4}=\frac{-12-8\sqrt{5}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{5}}{2*-4}=\frac{-12+8\sqrt{5}}{-8} $
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