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3x^2-(12x-3x+4x-1)/4=1
We move all terms to the left:
3x^2-(12x-3x+4x-1)/4-(1)=0
We add all the numbers together, and all the variables
3x^2-(13x-1)/4-1=0
We multiply all the terms by the denominator
3x^2*4-(13x-1)-1*4=0
We add all the numbers together, and all the variables
3x^2*4-(13x-1)-4=0
Wy multiply elements
12x^2-(13x-1)-4=0
We get rid of parentheses
12x^2-13x+1-4=0
We add all the numbers together, and all the variables
12x^2-13x-3=0
a = 12; b = -13; c = -3;
Δ = b2-4ac
Δ = -132-4·12·(-3)
Δ = 313
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{-(-13)-\sqrt{313}}{2*12}=\frac{13-\sqrt{313}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{313}}{2*12}=\frac{13+\sqrt{313}}{24} $
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