x=8/5x-21

Solution for x=8/5x-21 equation:

x=8/5x-21

We move all terms to the left:

x-(8/5x-21)=0


Domain of the equation: 5x-21)!=0

x∈R


We get rid of parentheses

x-8/5x+21=0

We multiply all the terms by the denominator


x*5x+21*5x-8=0

Wy multiply elements

5x^2+105x-8=0

a = 5; b = 105; c = -8;
Δ = b2-4ac
Δ = 1052-4·5·(-8)
Δ = 11185
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{-(105)-\sqrt{11185}}{2*5}=\frac{-105-\sqrt{11185}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{11185}}{2*5}=\frac{-105+\sqrt{11185}}{10}
$