3(5x)+8x=7/x+12-5x+7

Solution for 3(5x)+8x=7/x+12-5x+7 equation:

3(5x)+8x=7/x+12-5x+7

We move all terms to the left:

3(5x)+8x-(7/x+12-5x+7)=0


Domain of the equation: x+12-5x+7)!=0

We move all terms containing x to the left, all other terms to the right

x-5x+7)!=-12

x∈R


We add all the numbers together, and all the variables

35x+8x-(-5x+7/x+19)=0

We add all the numbers together, and all the variables

43x-(-5x+7/x+19)=0

We get rid of parentheses

43x+5x-7/x-19=0

We multiply all the terms by the denominator


43x*x+5x*x-19*x-7=0

We add all the numbers together, and all the variables

-19x+43x*x+5x*x-7=0

Wy multiply elements

43x^2+5x^2-19x-7=0

We add all the numbers together, and all the variables

48x^2-19x-7=0

a = 48; b = -19; c = -7;
Δ = b2-4ac
Δ = -192-4·48·(-7)
Δ = 1705
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{-(-19)-\sqrt{1705}}{2*48}=\frac{19-\sqrt{1705}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{1705}}{2*48}=\frac{19+\sqrt{1705}}{96}
$