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6x^2+19x+4=2x-1
We move all terms to the left:
6x^2+19x+4-(2x-1)=0
We get rid of parentheses
6x^2+19x-2x+1+4=0
We add all the numbers together, and all the variables
6x^2+17x+5=0
a = 6; b = 17; c = +5;
Δ = b2-4ac
Δ = 172-4·6·5
Δ = 169
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{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-13}{2*6}=\frac{-30}{12} =-2+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+13}{2*6}=\frac{-4}{12} =-1/3 $
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