4/5x+6=15x+4

Solution for 4/5x+6=15x+4 equation:

4/5x+6=15x+4

We move all terms to the left:

4/5x+6-(15x+4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-15x-4+6=0

We multiply all the terms by the denominator


-15x*5x-4*5x+6*5x+4=0

Wy multiply elements

-75x^2-20x+30x+4=0

We add all the numbers together, and all the variables

-75x^2+10x+4=0

a = -75; b = 10; c = +4;
Δ = b2-4ac
Δ = 102-4·(-75)·4
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{13}}{2*-75}=\frac{-10-10\sqrt{13}}{-150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{13}}{2*-75}=\frac{-10+10\sqrt{13}}{-150}
$