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17=5x^2-7x+4
We move all terms to the left:
17-(5x^2-7x+4)=0
We get rid of parentheses
-5x^2+7x-4+17=0
We add all the numbers together, and all the variables
-5x^2+7x+13=0
a = -5; b = 7; c = +13;
Δ = b2-4ac
Δ = 72-4·(-5)·13
Δ = 309
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{-(7)-\sqrt{309}}{2*-5}=\frac{-7-\sqrt{309}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{309}}{2*-5}=\frac{-7+\sqrt{309}}{-10} $
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