x+2/3(x)=280

Solution for x+2/3(x)=280 equation:

x+2/3(x)=280

We move all terms to the left:

x+2/3(x)-(280)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-280*3x+2=0

Wy multiply elements

3x^2-840x+2=0

a = 3; b = -840; c = +2;
Δ = b2-4ac
Δ = -8402-4·3·2
Δ = 705576
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:

$\sqrt{\Delta}=\sqrt{705576}=\sqrt{4*176394}=\sqrt{4}*\sqrt{176394}=2\sqrt{176394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-840)-2\sqrt{176394}}{2*3}=\frac{840-2\sqrt{176394}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-840)+2\sqrt{176394}}{2*3}=\frac{840+2\sqrt{176394}}{6}
$