4/5x+6=3x+4

Solution for 4/5x+6=3x+4 equation:

4/5x+6=3x+4

We move all terms to the left:

4/5x+6-(3x+4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-3x-4+6=0

We multiply all the terms by the denominator


-3x*5x-4*5x+6*5x+4=0

Wy multiply elements

-15x^2-20x+30x+4=0

We add all the numbers together, and all the variables

-15x^2+10x+4=0

a = -15; b = 10; c = +4;
Δ = b2-4ac
Δ = 102-4·(-15)·4
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{85}}{2*-15}=\frac{-10-2\sqrt{85}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{85}}{2*-15}=\frac{-10+2\sqrt{85}}{-30}
$