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7x^2+35x-17=445
We move all terms to the left:
7x^2+35x-17-(445)=0
We add all the numbers together, and all the variables
7x^2+35x-462=0
a = 7; b = 35; c = -462;
Δ = b2-4ac
Δ = 352-4·7·(-462)
Δ = 14161
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{14161}=119$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-119}{2*7}=\frac{-154}{14} =-11 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+119}{2*7}=\frac{84}{14} =6 $
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