2/3x-7+4x-1=90

Solution for 2/3x-7+4x-1=90 equation:

2/3x-7+4x-1=90

We move all terms to the left:

2/3x-7+4x-1-(90)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4x+2/3x-98=0

We multiply all the terms by the denominator


4x*3x-98*3x+2=0

Wy multiply elements

12x^2-294x+2=0

a = 12; b = -294; c = +2;
Δ = b2-4ac
Δ = -2942-4·12·2
Δ = 86340
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:

$\sqrt{\Delta}=\sqrt{86340}=\sqrt{4*21585}=\sqrt{4}*\sqrt{21585}=2\sqrt{21585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-294)-2\sqrt{21585}}{2*12}=\frac{294-2\sqrt{21585}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-294)+2\sqrt{21585}}{2*12}=\frac{294+2\sqrt{21585}}{24}
$