3x+7*8=2x/x-7

Solution for 3x+7*8=2x/x-7 equation:

3x+7*8=2x/x-7

We move all terms to the left:

3x+7*8-(2x/x-7)=0


Domain of the equation: x-7)!=0

x∈R


We add all the numbers together, and all the variables

3x-(2x/x-7)+56=0

We get rid of parentheses

3x-2x/x+7+56=0

We multiply all the terms by the denominator


3x*x-2x+7*x+56*x=0

We add all the numbers together, and all the variables

61x+3x*x=0

Wy multiply elements

3x^2+61x=0

a = 3; b = 61; c = 0;
Δ = b2-4ac
Δ = 612-4·3·0
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-61}{2*3}=\frac{-122}{6}
=-20+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+61}{2*3}=\frac{0}{6}
=0
$