5x+7=4/x-3

Solution for 5x+7=4/x-3 equation:

5x+7=4/x-3

We move all terms to the left:

5x+7-(4/x-3)=0


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

x∈R


We get rid of parentheses

5x-4/x+3+7=0

We multiply all the terms by the denominator


5x*x+3*x+7*x-4=0

We add all the numbers together, and all the variables

10x+5x*x-4=0

Wy multiply elements

5x^2+10x-4=0

a = 5; b = 10; c = -4;
Δ = b2-4ac
Δ = 102-4·5·(-4)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{5}}{2*5}=\frac{-10-6\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{5}}{2*5}=\frac{-10+6\sqrt{5}}{10}
$