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3x(4x-5)=12x-5

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Solution for 3x(4x-5)=12x-5 equation:



3x(4x-5)=12x-5
We move all terms to the left:
3x(4x-5)-(12x-5)=0
We multiply parentheses
12x^2-15x-(12x-5)=0
We get rid of parentheses
12x^2-15x-12x+5=0
We add all the numbers together, and all the variables
12x^2-27x+5=0
a = 12; b = -27; c = +5;
Δ = b2-4ac
Δ = -272-4·12·5
Δ = 489
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{-(-27)-\sqrt{489}}{2*12}=\frac{27-\sqrt{489}}{24}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{489}}{2*12}=\frac{27+\sqrt{489}}{24}

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