x=2/15x-4

Solution for x=2/15x-4 equation:

x=2/15x-4

We move all terms to the left:

x-(2/15x-4)=0


Domain of the equation: 15x-4)!=0

x∈R


We get rid of parentheses

x-2/15x+4=0

We multiply all the terms by the denominator


x*15x+4*15x-2=0

Wy multiply elements

15x^2+60x-2=0

a = 15; b = 60; c = -2;
Δ = b2-4ac
Δ = 602-4·15·(-2)
Δ = 3720
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:

$\sqrt{\Delta}=\sqrt{3720}=\sqrt{4*930}=\sqrt{4}*\sqrt{930}=2\sqrt{930}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{930}}{2*15}=\frac{-60-2\sqrt{930}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{930}}{2*15}=\frac{-60+2\sqrt{930}}{30}
$