4/5x=3x+121

Solution for 4/5x=3x+121 equation:

4/5x=3x+121

We move all terms to the left:

4/5x-(3x+121)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-3x-121=0

We multiply all the terms by the denominator


-3x*5x-121*5x+4=0

Wy multiply elements

-15x^2-605x+4=0

a = -15; b = -605; c = +4;
Δ = b2-4ac
Δ = -6052-4·(-15)·4
Δ = 366265
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{-(-605)-\sqrt{366265}}{2*-15}=\frac{605-\sqrt{366265}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-605)+\sqrt{366265}}{2*-15}=\frac{605+\sqrt{366265}}{-30}
$