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

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
$