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5x^2-4x-18=20
We move all terms to the left:
5x^2-4x-18-(20)=0
We add all the numbers together, and all the variables
5x^2-4x-38=0
a = 5; b = -4; c = -38;
Δ = b2-4ac
Δ = -42-4·5·(-38)
Δ = 776
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{194}}{2*5}=\frac{4-2\sqrt{194}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{194}}{2*5}=\frac{4+2\sqrt{194}}{10} $
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