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30x=2x^2-6x+25
We move all terms to the left:
30x-(2x^2-6x+25)=0
We get rid of parentheses
-2x^2+30x+6x-25=0
We add all the numbers together, and all the variables
-2x^2+36x-25=0
a = -2; b = 36; c = -25;
Δ = b2-4ac
Δ = 362-4·(-2)·(-25)
Δ = 1096
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1096}=\sqrt{4*274}=\sqrt{4}*\sqrt{274}=2\sqrt{274}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{274}}{2*-2}=\frac{-36-2\sqrt{274}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{274}}{2*-2}=\frac{-36+2\sqrt{274}}{-4} $
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