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15x+9x^2=24^2
We move all terms to the left:
15x+9x^2-(24^2)=0
We add all the numbers together, and all the variables
9x^2+15x-576=0
a = 9; b = 15; c = -576;
Δ = b2-4ac
Δ = 152-4·9·(-576)
Δ = 20961
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20961}=\sqrt{9*2329}=\sqrt{9}*\sqrt{2329}=3\sqrt{2329}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{2329}}{2*9}=\frac{-15-3\sqrt{2329}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{2329}}{2*9}=\frac{-15+3\sqrt{2329}}{18} $
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