5x+2x/5x=4+3/4

Solution for 5x+2x/5x=4+3/4 equation:

5x+2x/5x=4+3/4

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5x+2x/5x-4-3/4=0

We calculate fractions


5x+8x/20x+(-15x)/20x-4=0

We multiply all the terms by the denominator


5x*20x+8x+(-15x)-4*20x=0

We add all the numbers together, and all the variables

8x+5x*20x+(-15x)-4*20x=0

Wy multiply elements

100x^2+8x+(-15x)-80x=0

We get rid of parentheses

100x^2+8x-15x-80x=0

We add all the numbers together, and all the variables

100x^2-87x=0

a = 100; b = -87; c = 0;
Δ = b2-4ac
Δ = -872-4·100·0
Δ = 7569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7569}=87$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-87)-87}{2*100}=\frac{0}{200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87)+87}{2*100}=\frac{174}{200}
=87/100
$