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0=5x^2+8x-106
We move all terms to the left:
0-(5x^2+8x-106)=0
We add all the numbers together, and all the variables
-(5x^2+8x-106)=0
We get rid of parentheses
-5x^2-8x+106=0
a = -5; b = -8; c = +106;
Δ = b2-4ac
Δ = -82-4·(-5)·106
Δ = 2184
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2184}=\sqrt{4*546}=\sqrt{4}*\sqrt{546}=2\sqrt{546}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{546}}{2*-5}=\frac{8-2\sqrt{546}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{546}}{2*-5}=\frac{8+2\sqrt{546}}{-10} $
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