45x*5-47x=58x/74x+8

Solution for 45x*5-47x=58x/74x+8 equation:

45x*5-47x=58x/74x+8

We move all terms to the left:

45x*5-47x-(58x/74x+8)=0


Domain of the equation: 74x+8)!=0

x∈R


We add all the numbers together, and all the variables

-47x+45x*5-(58x/74x+8)=0

Wy multiply elements

-47x+225x-(58x/74x+8)=0

We get rid of parentheses

-47x+225x-58x/74x-8=0

We multiply all the terms by the denominator


-47x*74x+225x*74x-58x-8*74x=0

We add all the numbers together, and all the variables

-58x-47x*74x+225x*74x-8*74x=0

Wy multiply elements

-3478x^2+16650x^2-58x-592x=0

We add all the numbers together, and all the variables

13172x^2-650x=0

a = 13172; b = -650; c = 0;
Δ = b2-4ac
Δ = -6502-4·13172·0
Δ = 422500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{422500}=650$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-650)-650}{2*13172}=\frac{0}{26344}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-650)+650}{2*13172}=\frac{1300}{26344}
=325/6586
$