10x-(21-4x)=11-5(5x2)

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Solution for 10x-(21-4x)=11-5(5x2) equation:



10x-(21-4x)=11-5(5x^2)
We move all terms to the left:
10x-(21-4x)-(11-5(5x^2))=0
determiningTheFunctionDomain -(11-55x^2)+10x-(21-4x)=0
We add all the numbers together, and all the variables
-(11-55x^2)+10x-(-4x+21)=0
We get rid of parentheses
55x^2+10x+4x-11-21=0
We add all the numbers together, and all the variables
55x^2+14x-32=0
a = 55; b = 14; c = -32;
Δ = b2-4ac
Δ = 142-4·55·(-32)
Δ = 7236
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:
$\sqrt{\Delta}=\sqrt{7236}=\sqrt{36*201}=\sqrt{36}*\sqrt{201}=6\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{201}}{2*55}=\frac{-14-6\sqrt{201}}{110} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{201}}{2*55}=\frac{-14+6\sqrt{201}}{110} $

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