-x+4=9/7x-12

Solution for -x+4=9/7x-12 equation:

-x+4=9/7x-12

We move all terms to the left:

-x+4-(9/7x-12)=0


Domain of the equation: 7x-12)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(9/7x-12)+4=0

We get rid of parentheses

-1x-9/7x+12+4=0

We multiply all the terms by the denominator


-1x*7x+12*7x+4*7x-9=0

Wy multiply elements

-7x^2+84x+28x-9=0

We add all the numbers together, and all the variables

-7x^2+112x-9=0

a = -7; b = 112; c = -9;
Δ = b2-4ac
Δ = 1122-4·(-7)·(-9)
Δ = 12292
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:

$\sqrt{\Delta}=\sqrt{12292}=\sqrt{4*3073}=\sqrt{4}*\sqrt{3073}=2\sqrt{3073}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-2\sqrt{3073}}{2*-7}=\frac{-112-2\sqrt{3073}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+2\sqrt{3073}}{2*-7}=\frac{-112+2\sqrt{3073}}{-14}
$