2/7*x=280

Solution for 2/7*x=280 equation:

2/7*x=280

We move all terms to the left:

2/7*x-(280)=0


Domain of the equation: 7*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-280*7*x+2=0

Wy multiply elements

-1960x*x+2=0

Wy multiply elements

-1960x^2+2=0

a = -1960; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-1960)·2
Δ = 15680
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:

$\sqrt{\Delta}=\sqrt{15680}=\sqrt{3136*5}=\sqrt{3136}*\sqrt{5}=56\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-56\sqrt{5}}{2*-1960}=\frac{0-56\sqrt{5}}{-3920}
=-\frac{56\sqrt{5}}{-3920}
=-\frac{\sqrt{5}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+56\sqrt{5}}{2*-1960}=\frac{0+56\sqrt{5}}{-3920}
=\frac{56\sqrt{5}}{-3920}
=\frac{\sqrt{5}}{-70}
$