5/7x-4=x-12

Solution for 5/7x-4=x-12 equation:

5/7x-4=x-12

We move all terms to the left:

5/7x-4-(x-12)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

5/7x-x+12-4=0

We multiply all the terms by the denominator


-x*7x+12*7x-4*7x+5=0

Wy multiply elements

-7x^2+84x-28x+5=0

We add all the numbers together, and all the variables

-7x^2+56x+5=0

a = -7; b = 56; c = +5;
Δ = b2-4ac
Δ = 562-4·(-7)·5
Δ = 3276
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:

$\sqrt{\Delta}=\sqrt{3276}=\sqrt{36*91}=\sqrt{36}*\sqrt{91}=6\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-6\sqrt{91}}{2*-7}=\frac{-56-6\sqrt{91}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+6\sqrt{91}}{2*-7}=\frac{-56+6\sqrt{91}}{-14}
$