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((8-10x)(5x+4)-2)=0
We add all the numbers together, and all the variables
((-10x+8)(5x+4)-2)=0
We multiply parentheses ..
((-50x^2-40x+40x+32)-2)=0
We calculate terms in parentheses: +((-50x^2-40x+40x+32)-2), so:We get rid of parentheses
(-50x^2-40x+40x+32)-2
We get rid of parentheses
-50x^2-40x+40x+32-2
We add all the numbers together, and all the variables
-50x^2+30
Back to the equation:
+(-50x^2+30)
-50x^2+30=0
a = -50; b = 0; c = +30;
Δ = b2-4ac
Δ = 02-4·(-50)·30
Δ = 6000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{15}}{2*-50}=\frac{0-20\sqrt{15}}{-100} =-\frac{20\sqrt{15}}{-100} =-\frac{\sqrt{15}}{-5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{15}}{2*-50}=\frac{0+20\sqrt{15}}{-100} =\frac{20\sqrt{15}}{-100} =\frac{\sqrt{15}}{-5} $
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