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6x^2-31x+35=2/3
We move all terms to the left:
6x^2-31x+35-(2/3)=0
We add all the numbers together, and all the variables
6x^2-31x+35-(+2/3)=0
We get rid of parentheses
6x^2-31x+35-2/3=0
We multiply all the terms by the denominator
6x^2*3-31x*3-2+35*3=0
We add all the numbers together, and all the variables
6x^2*3-31x*3+103=0
Wy multiply elements
18x^2-93x+103=0
a = 18; b = -93; c = +103;
Δ = b2-4ac
Δ = -932-4·18·103
Δ = 1233
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1233}=\sqrt{9*137}=\sqrt{9}*\sqrt{137}=3\sqrt{137}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-93)-3\sqrt{137}}{2*18}=\frac{93-3\sqrt{137}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-93)+3\sqrt{137}}{2*18}=\frac{93+3\sqrt{137}}{36} $
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