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2x^2+17x=4x-6
We move all terms to the left:
2x^2+17x-(4x-6)=0
We get rid of parentheses
2x^2+17x-4x+6=0
We add all the numbers together, and all the variables
2x^2+13x+6=0
a = 2; b = 13; c = +6;
Δ = b2-4ac
Δ = 132-4·2·6
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-11}{2*2}=\frac{-24}{4} =-6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+11}{2*2}=\frac{-2}{4} =-1/2 $
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