(16/15)*x=26

Solution for (16/15)*x=26 equation:

(16/15)*x=26

We move all terms to the left:

(16/15)*x-(26)=0


Domain of the equation: 15)*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+16/15)*x-26=0

We multiply parentheses

16x^2-26=0

a = 16; b = 0; c = -26;
Δ = b2-4ac
Δ = 02-4·16·(-26)
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{26}}{2*16}=\frac{0-8\sqrt{26}}{32}
=-\frac{8\sqrt{26}}{32}
=-\frac{\sqrt{26}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{26}}{2*16}=\frac{0+8\sqrt{26}}{32}
=\frac{8\sqrt{26}}{32}
=\frac{\sqrt{26}}{4}
$