2.5(x)=2x^2/3x+7

Solution for 2.5(x)=2x^2/3x+7 equation:

2.5(x)=2x^2/3x+7

We move all terms to the left:

2.5(x)-(2x^2/3x+7)=0


Domain of the equation: 3x+7)!=0

x∈R


We get rid of parentheses

-2x^2/3x+2.5x-7=0

We multiply all the terms by the denominator


-2x^2+(2.5x)*3x-7*3x=0

We add all the numbers together, and all the variables

-2x^2+(+2.5x)*3x-7*3x=0

We multiply parentheses

-2x^2+6x^2-7*3x=0

Wy multiply elements

-2x^2+6x^2-21x=0

We add all the numbers together, and all the variables

4x^2-21x=0

a = 4; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·4·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*4}=\frac{42}{8}
=5+1/4
$