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25x-10=-25x^2-50x+200
We move all terms to the left:
25x-10-(-25x^2-50x+200)=0
We get rid of parentheses
25x^2+50x+25x-200-10=0
We add all the numbers together, and all the variables
25x^2+75x-210=0
a = 25; b = 75; c = -210;
Δ = b2-4ac
Δ = 752-4·25·(-210)
Δ = 26625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{26625}=\sqrt{25*1065}=\sqrt{25}*\sqrt{1065}=5\sqrt{1065}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-5\sqrt{1065}}{2*25}=\frac{-75-5\sqrt{1065}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+5\sqrt{1065}}{2*25}=\frac{-75+5\sqrt{1065}}{50} $
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