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5x^2-3x+8=12
We move all terms to the left:
5x^2-3x+8-(12)=0
We add all the numbers together, and all the variables
5x^2-3x-4=0
a = 5; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·5·(-4)
Δ = 89
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{-(-3)-\sqrt{89}}{2*5}=\frac{3-\sqrt{89}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*5}=\frac{3+\sqrt{89}}{10} $
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