7=5x-20/3x-10

Solution for 7=5x-20/3x-10 equation:

7=5x-20/3x-10

We move all terms to the left:

7-(5x-20/3x-10)=0


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

x∈R


We get rid of parentheses

-5x+20/3x+10+7=0

We multiply all the terms by the denominator


-5x*3x+10*3x+7*3x+20=0

Wy multiply elements

-15x^2+30x+21x+20=0

We add all the numbers together, and all the variables

-15x^2+51x+20=0

a = -15; b = 51; c = +20;
Δ = b2-4ac
Δ = 512-4·(-15)·20
Δ = 3801
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{-(51)-\sqrt{3801}}{2*-15}=\frac{-51-\sqrt{3801}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+\sqrt{3801}}{2*-15}=\frac{-51+\sqrt{3801}}{-30}
$