4/5x+7/4x=2

Solution for 4/5x+7/4x=2 equation:

4/5x+7/4x=2

We move all terms to the left:

4/5x+7/4x-(2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


16x/20x^2+35x/20x^2-2=0

We multiply all the terms by the denominator


16x+35x-2*20x^2=0

We add all the numbers together, and all the variables

51x-2*20x^2=0

Wy multiply elements

-40x^2+51x=0

a = -40; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·(-40)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*-40}=\frac{-102}{-80}
=1+11/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*-40}=\frac{0}{-80}
=0
$