2/3X+7/2x=5

Solution for 2/3X+7/2x=5 equation:

2/3X+7/2X=5

We move all terms to the left:

2/3X+7/2X-(5)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R



Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We calculate fractions


4X/6X^2+21X/6X^2-5=0

We multiply all the terms by the denominator


4X+21X-5*6X^2=0

We add all the numbers together, and all the variables

25X-5*6X^2=0

Wy multiply elements

-30X^2+25X=0

a = -30; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-30)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-30}=\frac{-50}{-60}
=5/6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-30}=\frac{0}{-60}
=0
$