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0=-5x^2+8x+3
We move all terms to the left:
0-(-5x^2+8x+3)=0
We add all the numbers together, and all the variables
-(-5x^2+8x+3)=0
We get rid of parentheses
5x^2-8x-3=0
a = 5; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·5·(-3)
Δ = 124
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{31}}{2*5}=\frac{8-2\sqrt{31}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{31}}{2*5}=\frac{8+2\sqrt{31}}{10} $
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