9(13-x)-4x=5x(21-2x)+9x

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Solution for 9(13-x)-4x=5x(21-2x)+9x equation:



9(13-x)-4x=5x(21-2x)+9x
We move all terms to the left:
9(13-x)-4x-(5x(21-2x)+9x)=0
We add all the numbers together, and all the variables
9(-1x+13)-4x-(5x(-2x+21)+9x)=0
We add all the numbers together, and all the variables
-4x+9(-1x+13)-(5x(-2x+21)+9x)=0
We multiply parentheses
-4x-9x-(5x(-2x+21)+9x)+117=0
We calculate terms in parentheses: -(5x(-2x+21)+9x), so:
5x(-2x+21)+9x
We add all the numbers together, and all the variables
9x+5x(-2x+21)
We multiply parentheses
-10x^2+9x+105x
We add all the numbers together, and all the variables
-10x^2+114x
Back to the equation:
-(-10x^2+114x)
We add all the numbers together, and all the variables
-(-10x^2+114x)-13x+117=0
We get rid of parentheses
10x^2-114x-13x+117=0
We add all the numbers together, and all the variables
10x^2-127x+117=0
a = 10; b = -127; c = +117;
Δ = b2-4ac
Δ = -1272-4·10·117
Δ = 11449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11449}=107$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-127)-107}{2*10}=\frac{20}{20} =1 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-127)+107}{2*10}=\frac{234}{20} =11+7/10 $

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