x=14/3x-15

Solution for x=14/3x-15 equation:

x=14/3x-15

We move all terms to the left:

x-(14/3x-15)=0


Domain of the equation: 3x-15)!=0

x∈R


We get rid of parentheses

x-14/3x+15=0

We multiply all the terms by the denominator


x*3x+15*3x-14=0

Wy multiply elements

3x^2+45x-14=0

a = 3; b = 45; c = -14;
Δ = b2-4ac
Δ = 452-4·3·(-14)
Δ = 2193
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{-(45)-\sqrt{2193}}{2*3}=\frac{-45-\sqrt{2193}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2193}}{2*3}=\frac{-45+\sqrt{2193}}{6}
$