3x+1/5x+4-x+7=88

Solution for 3x+1/5x+4-x+7=88 equation:

3x+1/5x+4-x+7=88

We move all terms to the left:

3x+1/5x+4-x+7-(88)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/5x-77=0

We multiply all the terms by the denominator


2x*5x-77*5x+1=0

Wy multiply elements

10x^2-385x+1=0

a = 10; b = -385; c = +1;
Δ = b2-4ac
Δ = -3852-4·10·1
Δ = 148185
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:

$\sqrt{\Delta}=\sqrt{148185}=\sqrt{9*16465}=\sqrt{9}*\sqrt{16465}=3\sqrt{16465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-385)-3\sqrt{16465}}{2*10}=\frac{385-3\sqrt{16465}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-385)+3\sqrt{16465}}{2*10}=\frac{385+3\sqrt{16465}}{20}
$