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25x^2+5x=625x+225
We move all terms to the left:
25x^2+5x-(625x+225)=0
We get rid of parentheses
25x^2+5x-625x-225=0
We add all the numbers together, and all the variables
25x^2-620x-225=0
a = 25; b = -620; c = -225;
Δ = b2-4ac
Δ = -6202-4·25·(-225)
Δ = 406900
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{406900}=\sqrt{100*4069}=\sqrt{100}*\sqrt{4069}=10\sqrt{4069}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-620)-10\sqrt{4069}}{2*25}=\frac{620-10\sqrt{4069}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-620)+10\sqrt{4069}}{2*25}=\frac{620+10\sqrt{4069}}{50} $
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