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2x^2-11x=17-x2
We move all terms to the left:
2x^2-11x-(17-x2)=0
We add all the numbers together, and all the variables
2x^2-(-1x^2+17)-11x=0
We get rid of parentheses
2x^2+1x^2-11x-17=0
We add all the numbers together, and all the variables
3x^2-11x-17=0
a = 3; b = -11; c = -17;
Δ = b2-4ac
Δ = -112-4·3·(-17)
Δ = 325
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5\sqrt{13}}{2*3}=\frac{11-5\sqrt{13}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5\sqrt{13}}{2*3}=\frac{11+5\sqrt{13}}{6} $
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