5x-3/4+5(x+5)+3(13-2x)x=3

Solution for 5x-3/4+5(x+5)+3(13-2x)x=3 equation:

5x-3/4+5(x+5)+3(13-2x)x=3

We move all terms to the left:

5x-3/4+5(x+5)+3(13-2x)x-(3)=0

determiningTheFunctionDomain
5x+5(x+5)+3(13-2x)x-3-3/4=0

We add all the numbers together, and all the variables

5x+5(x+5)+3(-2x+13)x-3-3/4=0

We multiply parentheses

-6x^2+5x+5x+39x+25-3-3/4=0

We multiply all the terms by the denominator


-6x^2*4+5x*4+5x*4+39x*4-3+25*4-3*4=0

We add all the numbers together, and all the variables

-6x^2*4+5x*4+5x*4+39x*4+85=0

Wy multiply elements

-24x^2+20x+20x+156x+85=0

We add all the numbers together, and all the variables

-24x^2+196x+85=0

a = -24; b = 196; c = +85;
Δ = b2-4ac
Δ = 1962-4·(-24)·85
Δ = 46576
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:

$\sqrt{\Delta}=\sqrt{46576}=\sqrt{16*2911}=\sqrt{16}*\sqrt{2911}=4\sqrt{2911}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(196)-4\sqrt{2911}}{2*-24}=\frac{-196-4\sqrt{2911}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(196)+4\sqrt{2911}}{2*-24}=\frac{-196+4\sqrt{2911}}{-48}
$