5(x-2)/3=-x*

Solution for 5(x-2)/3=-x* equation:

5(x-2)/3=-x*

We move all terms to the left:

5(x-2)/3-(-x*)=0

We get rid of parentheses

5(x-2)/3+x*=0

We multiply all the terms by the denominator


5(x-2)+(x*)*3=0

We add all the numbers together, and all the variables

5(x-2)+(+x*)*3=0

We multiply parentheses

3x^2+5x-10=0

a = 3; b = 5; c = -10;
Δ = b2-4ac
Δ = 52-4·3·(-10)
Δ = 145
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{-(5)-\sqrt{145}}{2*3}=\frac{-5-\sqrt{145}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{145}}{2*3}=\frac{-5+\sqrt{145}}{6}
$