(2/3)x-7=35-4x

Solution for (2/3)x-7=35-4x equation:

(2/3)x-7=35-4x

We move all terms to the left:

(2/3)x-7-(35-4x)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/3)x-(-4x+35)-7=0

We multiply parentheses

2x^2-(-4x+35)-7=0

We get rid of parentheses

2x^2+4x-35-7=0

We add all the numbers together, and all the variables

2x^2+4x-42=0

a = 2; b = 4; c = -42;
Δ = b2-4ac
Δ = 42-4·2·(-42)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{22}}{2*2}=\frac{-4-4\sqrt{22}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{22}}{2*2}=\frac{-4+4\sqrt{22}}{4}
$