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3x(2x-7)=5x+17+x
We move all terms to the left:
3x(2x-7)-(5x+17+x)=0
We add all the numbers together, and all the variables
3x(2x-7)-(6x+17)=0
We multiply parentheses
6x^2-21x-(6x+17)=0
We get rid of parentheses
6x^2-21x-6x-17=0
We add all the numbers together, and all the variables
6x^2-27x-17=0
a = 6; b = -27; c = -17;
Δ = b2-4ac
Δ = -272-4·6·(-17)
Δ = 1137
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{1137}}{2*6}=\frac{27-\sqrt{1137}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{1137}}{2*6}=\frac{27+\sqrt{1137}}{12} $
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