2/3x-5=4x+10

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Solution for 2/3x-5=4x+10 equation: 



2/3x-5=4x+10

We move all terms to the left:

2/3x-5-(4x+10)=0



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We get rid of parentheses

2/3x-4x-10-5=0

We multiply all the terms by the denominator


-4x*3x-10*3x-5*3x+2=0

Wy multiply elements

-12x^2-30x-15x+2=0

We add all the numbers together, and all the variables

-12x^2-45x+2=0

a = -12; b = -45; c = +2;
Δ = b2-4ac
Δ = -452-4·(-12)·2
Δ = 2121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2121}}{2*-12}=\frac{45-\sqrt{2121}}{-24}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2121}}{2*-12}=\frac{45+\sqrt{2121}}{-24}
$

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