4/5x+7=9x+2

Solution for 4/5x+7=9x+2 equation:

4/5x+7=9x+2

We move all terms to the left:

4/5x+7-(9x+2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-9x-2+7=0

We multiply all the terms by the denominator


-9x*5x-2*5x+7*5x+4=0

Wy multiply elements

-45x^2-10x+35x+4=0

We add all the numbers together, and all the variables

-45x^2+25x+4=0

a = -45; b = 25; c = +4;
Δ = b2-4ac
Δ = 252-4·(-45)·4
Δ = 1345
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{-(25)-\sqrt{1345}}{2*-45}=\frac{-25-\sqrt{1345}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{1345}}{2*-45}=\frac{-25+\sqrt{1345}}{-90}
$