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5x^2+15x-93=-3
We move all terms to the left:
5x^2+15x-93-(-3)=0
We add all the numbers together, and all the variables
5x^2+15x-90=0
a = 5; b = 15; c = -90;
Δ = b2-4ac
Δ = 152-4·5·(-90)
Δ = 2025
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{2025}=45$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-45}{2*5}=\frac{-60}{10} =-6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+45}{2*5}=\frac{30}{10} =3 $
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