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17-7(x-3)x=4
We move all terms to the left:
17-7(x-3)x-(4)=0
We add all the numbers together, and all the variables
-7(x-3)x+13=0
We multiply parentheses
-7x^2+21x+13=0
a = -7; b = 21; c = +13;
Δ = b2-4ac
Δ = 212-4·(-7)·13
Δ = 805
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{-(21)-\sqrt{805}}{2*-7}=\frac{-21-\sqrt{805}}{-14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{805}}{2*-7}=\frac{-21+\sqrt{805}}{-14} $
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