7x-(4x-4)=1/3x-10

Solution for 7x-(4x-4)=1/3x-10 equation:

7x-(4x-4)=1/3x-10

We move all terms to the left:

7x-(4x-4)-(1/3x-10)=0


Domain of the equation: 3x-10)!=0

x∈R


We get rid of parentheses

7x-4x-1/3x+4+10=0

We multiply all the terms by the denominator


7x*3x-4x*3x+4*3x+10*3x-1=0

Wy multiply elements

21x^2-12x^2+12x+30x-1=0

We add all the numbers together, and all the variables

9x^2+42x-1=0

a = 9; b = 42; c = -1;
Δ = b2-4ac
Δ = 422-4·9·(-1)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-30\sqrt{2}}{2*9}=\frac{-42-30\sqrt{2}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+30\sqrt{2}}{2*9}=\frac{-42+30\sqrt{2}}{18}
$