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4x(3x-4)=x+2/4
We move all terms to the left:
4x(3x-4)-(x+2/4)=0
We add all the numbers together, and all the variables
4x(3x-4)-(+x+2/4)=0
We multiply parentheses
12x^2-16x-(+x+2/4)=0
We get rid of parentheses
12x^2-16x-x-2/4=0
We multiply all the terms by the denominator
12x^2*4-16x*4-x*4-2=0
Wy multiply elements
48x^2-64x-4x-2=0
We add all the numbers together, and all the variables
48x^2-68x-2=0
a = 48; b = -68; c = -2;
Δ = b2-4ac
Δ = -682-4·48·(-2)
Δ = 5008
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5008}=\sqrt{16*313}=\sqrt{16}*\sqrt{313}=4\sqrt{313}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{313}}{2*48}=\frac{68-4\sqrt{313}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{313}}{2*48}=\frac{68+4\sqrt{313}}{96} $
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