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6-4x=3x^2-10x+2
We move all terms to the left:
6-4x-(3x^2-10x+2)=0
We get rid of parentheses
-3x^2-4x+10x-2+6=0
We add all the numbers together, and all the variables
-3x^2+6x+4=0
a = -3; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·(-3)·4
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*-3}=\frac{-6-2\sqrt{21}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*-3}=\frac{-6+2\sqrt{21}}{-6} $
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