2x+5=5/3x-10=7

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Solution for 2x+5=5/3x-10=7 equation: 



2x+5=5/3x-10=7

We move all terms to the left:

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



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

x∈R



We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2+30x+15x-5=0

We add all the numbers together, and all the variables

6x^2+45x-5=0

a = 6; b = 45; c = -5;
Δ = b2-4ac
Δ = 452-4·6·(-5)
Δ = 2145
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{2145}}{2*6}=\frac{-45-\sqrt{2145}}{12}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2145}}{2*6}=\frac{-45+\sqrt{2145}}{12}
$

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