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x(3x+7)=29
We move all terms to the left:
x(3x+7)-(29)=0
We multiply parentheses
3x^2+7x-29=0
a = 3; b = 7; c = -29;
Δ = b2-4ac
Δ = 72-4·3·(-29)
Δ = 397
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{397}}{2*3}=\frac{-7-\sqrt{397}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{397}}{2*3}=\frac{-7+\sqrt{397}}{6} $
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