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2x+19=4x^2-4x+1
We move all terms to the left:
2x+19-(4x^2-4x+1)=0
We get rid of parentheses
-4x^2+2x+4x-1+19=0
We add all the numbers together, and all the variables
-4x^2+6x+18=0
a = -4; b = 6; c = +18;
Δ = b2-4ac
Δ = 62-4·(-4)·18
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*-4}=\frac{-24}{-8} =+3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*-4}=\frac{12}{-8} =-1+1/2 $
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