2/5x+7/4x=90

Solution for 2/5x+7/4x=90 equation:

2/5x+7/4x=90

We move all terms to the left:

2/5x+7/4x-(90)=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


8x/20x^2+35x/20x^2-90=0

We multiply all the terms by the denominator


8x+35x-90*20x^2=0

We add all the numbers together, and all the variables

43x-90*20x^2=0

Wy multiply elements

-1800x^2+43x=0

a = -1800; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·(-1800)·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*-1800}=\frac{-86}{-3600}
=43/1800
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*-1800}=\frac{0}{-3600}
=0
$