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25x^2+15x-24=0
a = 25; b = 15; c = -24;
Δ = b2-4ac
Δ = 152-4·25·(-24)
Δ = 2625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2625}=\sqrt{25*105}=\sqrt{25}*\sqrt{105}=5\sqrt{105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{105}}{2*25}=\frac{-15-5\sqrt{105}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{105}}{2*25}=\frac{-15+5\sqrt{105}}{50} $
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