-(4-x)=(3/4)(x-6)

Solution for -(4-x)=(3/4)(x-6) equation:

-(4-x)=(3/4)(x-6)

We move all terms to the left:

-(4-x)-((3/4)(x-6))=0


Domain of the equation: 4)(x-6))!=0

x∈R


We add all the numbers together, and all the variables

-(-1x+4)-((+3/4)(x-6))=0

We get rid of parentheses

1x-((+3/4)(x-6))-4=0

We multiply parentheses ..

-((+3x^2+3/4*-6))+1x-4=0

We multiply all the terms by the denominator


-((+3x^2+3+1x*4*-6))-4*4*-6))=0


We calculate terms in parentheses: -((+3x^2+3+1x*4*-6)), so:

(+3x^2+3+1x*4*-6)

We get rid of parentheses

3x^2+1x*4*+3-6

We add all the numbers together, and all the variables

3x^2+1x*4*-3

Wy multiply elements

3x^2+4x^2-3

We add all the numbers together, and all the variables

7x^2-3

Back to the equation:

-(7x^2-3)


We add all the numbers together, and all the variables

-(7x^2-3)=0

We get rid of parentheses

-7x^2+3=0

a = -7; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-7)·3
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*-7}=\frac{0-2\sqrt{21}}{-14}
=-\frac{2\sqrt{21}}{-14}
=-\frac{\sqrt{21}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*-7}=\frac{0+2\sqrt{21}}{-14}
=\frac{2\sqrt{21}}{-14}
=\frac{\sqrt{21}}{-7}
$