4/5x=x+90

Solution for 4/5x=x+90 equation:

4/5x=x+90

We move all terms to the left:

4/5x-(x+90)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-x-90=0

We multiply all the terms by the denominator


-x*5x-90*5x+4=0

Wy multiply elements

-5x^2-450x+4=0

a = -5; b = -450; c = +4;
Δ = b2-4ac
Δ = -4502-4·(-5)·4
Δ = 202580
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:

$\sqrt{\Delta}=\sqrt{202580}=\sqrt{4*50645}=\sqrt{4}*\sqrt{50645}=2\sqrt{50645}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-2\sqrt{50645}}{2*-5}=\frac{450-2\sqrt{50645}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+2\sqrt{50645}}{2*-5}=\frac{450+2\sqrt{50645}}{-10}
$