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x(4x.x-3)=1/5
We move all terms to the left:
x(4x.x-3)-(1/5)=0
We add all the numbers together, and all the variables
x(4x.x-3)-(+1/5)=0
We multiply parentheses
4x^2-3x-(+1/5)=0
We get rid of parentheses
4x^2-3x-1/5=0
We multiply all the terms by the denominator
4x^2*5-3x*5-1=0
Wy multiply elements
20x^2-15x-1=0
a = 20; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·20·(-1)
Δ = 305
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{-(-15)-\sqrt{305}}{2*20}=\frac{15-\sqrt{305}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{305}}{2*20}=\frac{15+\sqrt{305}}{40} $
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