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5(-2x-4)5x+5=15
We move all terms to the left:
5(-2x-4)5x+5-(15)=0
We add all the numbers together, and all the variables
5(-2x-4)5x-10=0
We multiply parentheses
-50x^2-100x-10=0
a = -50; b = -100; c = -10;
Δ = b2-4ac
Δ = -1002-4·(-50)·(-10)
Δ = 8000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-40\sqrt{5}}{2*-50}=\frac{100-40\sqrt{5}}{-100} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+40\sqrt{5}}{2*-50}=\frac{100+40\sqrt{5}}{-100} $
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