-2(-x+5)5x+2=27

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Solution for -2(-x+5)5x+2=27 equation:



-2(-x+5)5x+2=27
We move all terms to the left:
-2(-x+5)5x+2-(27)=0
We add all the numbers together, and all the variables
-2(-1x+5)5x+2-27=0
We add all the numbers together, and all the variables
-2(-1x+5)5x-25=0
We multiply parentheses
10x^2-50x-25=0
a = 10; b = -50; c = -25;
Δ = b2-4ac
Δ = -502-4·10·(-25)
Δ = 3500
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:
$\sqrt{\Delta}=\sqrt{3500}=\sqrt{100*35}=\sqrt{100}*\sqrt{35}=10\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{35}}{2*10}=\frac{50-10\sqrt{35}}{20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{35}}{2*10}=\frac{50+10\sqrt{35}}{20} $

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