-2/3x+3(-5x+40)=-34

Solution for -2/3x+3(-5x+40)=-34 equation:

-2/3x+3(-5x+40)=-34

We move all terms to the left:

-2/3x+3(-5x+40)-(-34)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-2/3x+3(-5x+40)+34=0

We multiply parentheses

-2/3x-15x+120+34=0

We multiply all the terms by the denominator


-15x*3x+120*3x+34*3x-2=0

Wy multiply elements

-45x^2+360x+102x-2=0

We add all the numbers together, and all the variables

-45x^2+462x-2=0

a = -45; b = 462; c = -2;
Δ = b2-4ac
Δ = 4622-4·(-45)·(-2)
Δ = 213084
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:

$\sqrt{\Delta}=\sqrt{213084}=\sqrt{36*5919}=\sqrt{36}*\sqrt{5919}=6\sqrt{5919}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(462)-6\sqrt{5919}}{2*-45}=\frac{-462-6\sqrt{5919}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(462)+6\sqrt{5919}}{2*-45}=\frac{-462+6\sqrt{5919}}{-90}
$