x=(3/8)(x-21)

Solution for x=(3/8)(x-21) equation:

x=(3/8)(x-21)

We move all terms to the left:

x-((3/8)(x-21))=0


Domain of the equation: 8)(x-21))!=0

x∈R


We add all the numbers together, and all the variables

x-((+3/8)(x-21))=0

We multiply parentheses ..

-((+3x^2+3/8*-21))+x=0

We multiply all the terms by the denominator


-((+3x^2+3+x*8*-21))=0


We calculate terms in parentheses: -((+3x^2+3+x*8*-21)), so:

(+3x^2+3+x*8*-21)

We get rid of parentheses

3x^2+x*8*+3-21

We add all the numbers together, and all the variables

3x^2+x*8*-18

Wy multiply elements

3x^2+8x^2-18

We add all the numbers together, and all the variables

11x^2-18

Back to the equation:

-(11x^2-18)


We get rid of parentheses

-11x^2+18=0

a = -11; b = 0; c = +18;
Δ = b2-4ac
Δ = 02-4·(-11)·18
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{22}}{2*-11}=\frac{0-6\sqrt{22}}{-22}
=-\frac{6\sqrt{22}}{-22}
=-\frac{3\sqrt{22}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{22}}{2*-11}=\frac{0+6\sqrt{22}}{-22}
=\frac{6\sqrt{22}}{-22}
=\frac{3\sqrt{22}}{-11}
$