(4/9)x+(1/5)x=87

Solution for (4/9)x+(1/5)x=87 equation:

(4/9)x+(1/5)x=87

We move all terms to the left:

(4/9)x+(1/5)x-(87)=0


Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+4/9)x+(+1/5)x-87=0

We multiply parentheses

4x^2+x^2-87=0

We add all the numbers together, and all the variables

5x^2-87=0

a = 5; b = 0; c = -87;
Δ = b2-4ac
Δ = 02-4·5·(-87)
Δ = 1740
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:

$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{435}}{2*5}=\frac{0-2\sqrt{435}}{10}
=-\frac{2\sqrt{435}}{10}
=-\frac{\sqrt{435}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{435}}{2*5}=\frac{0+2\sqrt{435}}{10}
=\frac{2\sqrt{435}}{10}
=\frac{\sqrt{435}}{5}
$