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3x(4x-5)-3x=3
We move all terms to the left:
3x(4x-5)-3x-(3)=0
We add all the numbers together, and all the variables
-3x+3x(4x-5)-3=0
We multiply parentheses
12x^2-3x-15x-3=0
We add all the numbers together, and all the variables
12x^2-18x-3=0
a = 12; b = -18; c = -3;
Δ = b2-4ac
Δ = -182-4·12·(-3)
Δ = 468
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{13}}{2*12}=\frac{18-6\sqrt{13}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{13}}{2*12}=\frac{18+6\sqrt{13}}{24} $
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