4/5x-9=3x+3-7x

Solution for 4/5x-9=3x+3-7x equation:

4/5x-9=3x+3-7x

We move all terms to the left:

4/5x-9-(3x+3-7x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-(-4x+3)-9=0

We get rid of parentheses

4/5x+4x-3-9=0

We multiply all the terms by the denominator


4x*5x-3*5x-9*5x+4=0

Wy multiply elements

20x^2-15x-45x+4=0

We add all the numbers together, and all the variables

20x^2-60x+4=0

a = 20; b = -60; c = +4;
Δ = b2-4ac
Δ = -602-4·20·4
Δ = 3280
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:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{205}}{2*20}=\frac{60-4\sqrt{205}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{205}}{2*20}=\frac{60+4\sqrt{205}}{40}
$