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3x(x+5)=17
We move all terms to the left:
3x(x+5)-(17)=0
We multiply parentheses
3x^2+15x-17=0
a = 3; b = 15; c = -17;
Δ = b2-4ac
Δ = 152-4·3·(-17)
Δ = 429
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{-(15)-\sqrt{429}}{2*3}=\frac{-15-\sqrt{429}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{429}}{2*3}=\frac{-15+\sqrt{429}}{6} $
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