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4(x-1)(2x-1)+4(2x-1)(3x-1)+4(3x-1)(4x-1)=53x^2
We move all terms to the left:
4(x-1)(2x-1)+4(2x-1)(3x-1)+4(3x-1)(4x-1)-(53x^2)=0
determiningTheFunctionDomain -53x^2+4(x-1)(2x-1)+4(2x-1)(3x-1)+4(3x-1)(4x-1)=0
We multiply parentheses ..
-53x^2+4(+2x^2-1x-2x+1)+4(2x-1)(3x-1)+4(3x-1)(4x-1)=0
We multiply parentheses
-53x^2+8x^2-4x-8x+4(2x-1)(3x-1)+4(3x-1)(4x-1)+4=0
We multiply parentheses ..
-53x^2+8x^2+4(+6x^2-2x-3x+1)-4x-8x+4(3x-1)(4x-1)+4=0
We add all the numbers together, and all the variables
-45x^2+4(+6x^2-2x-3x+1)-12x+4(3x-1)(4x-1)+4=0
We multiply parentheses
-45x^2+24x^2-8x-12x-12x+4(3x-1)(4x-1)+4+4=0
We multiply parentheses ..
-45x^2+24x^2+4(+12x^2-3x-4x+1)-8x-12x-12x+4+4=0
We add all the numbers together, and all the variables
-21x^2+4(+12x^2-3x-4x+1)-32x+8=0
We multiply parentheses
-21x^2+48x^2-12x-16x-32x+4+8=0
We add all the numbers together, and all the variables
27x^2-60x+12=0
a = 27; b = -60; c = +12;
Δ = b2-4ac
Δ = -602-4·27·12
Δ = 2304
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2304}=48$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-48}{2*27}=\frac{12}{54} =2/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+48}{2*27}=\frac{108}{54} =2 $
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