8/15*x=16

Solution for 8/15*x=16 equation:

8/15*x=16

We move all terms to the left:

8/15*x-(16)=0


Domain of the equation: 15*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-16*15*x+8=0

Wy multiply elements

-240x*x+8=0

Wy multiply elements

-240x^2+8=0

a = -240; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-240)·8
Δ = 7680
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:

$\sqrt{\Delta}=\sqrt{7680}=\sqrt{256*30}=\sqrt{256}*\sqrt{30}=16\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{30}}{2*-240}=\frac{0-16\sqrt{30}}{-480}
=-\frac{16\sqrt{30}}{-480}
=-\frac{\sqrt{30}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{30}}{2*-240}=\frac{0+16\sqrt{30}}{-480}
=\frac{16\sqrt{30}}{-480}
=\frac{\sqrt{30}}{-30}
$