2x+5x(26-x)=100

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Solution for 2x+5x(26-x)=100 equation:



2x+5x(26-x)=100
We move all terms to the left:
2x+5x(26-x)-(100)=0
We add all the numbers together, and all the variables
2x+5x(-1x+26)-100=0
We multiply parentheses
-5x^2+2x+130x-100=0
We add all the numbers together, and all the variables
-5x^2+132x-100=0
a = -5; b = 132; c = -100;
Δ = b2-4ac
Δ = 1322-4·(-5)·(-100)
Δ = 15424
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:
$\sqrt{\Delta}=\sqrt{15424}=\sqrt{64*241}=\sqrt{64}*\sqrt{241}=8\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-8\sqrt{241}}{2*-5}=\frac{-132-8\sqrt{241}}{-10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+8\sqrt{241}}{2*-5}=\frac{-132+8\sqrt{241}}{-10} $

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