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6x^2-4x+1=-9x+5
We move all terms to the left:
6x^2-4x+1-(-9x+5)=0
We get rid of parentheses
6x^2-4x+9x-5+1=0
We add all the numbers together, and all the variables
6x^2+5x-4=0
a = 6; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·6·(-4)
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*6}=\frac{-16}{12} =-1+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*6}=\frac{6}{12} =1/2 $
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