(3/4)x-2+90+(2/5)x=180

Solution for (3/4)x-2+90+(2/5)x=180 equation:

(3/4)x-2+90+(2/5)x=180

We move all terms to the left:

(3/4)x-2+90+(2/5)x-(180)=0


Domain of the equation: 4)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

(+3/4)x+(+2/5)x-2+90-180=0

We add all the numbers together, and all the variables

(+3/4)x+(+2/5)x-92=0

We multiply parentheses

3x^2+2x^2-92=0

We add all the numbers together, and all the variables

5x^2-92=0

a = 5; b = 0; c = -92;
Δ = b2-4ac
Δ = 02-4·5·(-92)
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{115}}{2*5}=\frac{0-4\sqrt{115}}{10}
=-\frac{4\sqrt{115}}{10}
=-\frac{2\sqrt{115}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{115}}{2*5}=\frac{0+4\sqrt{115}}{10}
=\frac{4\sqrt{115}}{10}
=\frac{2\sqrt{115}}{5}
$