4/3x+7=2.5x

Solution for 4/3x+7=2.5x equation:

4/3x+7=2.5x

We move all terms to the left:

4/3x+7-(2.5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-(+2.5x)+7=0

We get rid of parentheses

4/3x-2.5x+7=0

We multiply all the terms by the denominator


-(2.5x)*3x+7*3x+4=0

We add all the numbers together, and all the variables

-(+2.5x)*3x+7*3x+4=0

We multiply parentheses

-6x^2+7*3x+4=0

Wy multiply elements

-6x^2+21x+4=0

a = -6; b = 21; c = +4;
Δ = b2-4ac
Δ = 212-4·(-6)·4
Δ = 537
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{537}}{2*-6}=\frac{-21-\sqrt{537}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{537}}{2*-6}=\frac{-21+\sqrt{537}}{-12}
$