(15/4)x=14

Solution for (15/4)x=14 equation:

(15/4)x=14

We move all terms to the left:

(15/4)x-(14)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+15/4)x-14=0

We multiply parentheses

15x^2-14=0

a = 15; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·15·(-14)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*15}=\frac{0-2\sqrt{210}}{30}
=-\frac{2\sqrt{210}}{30}
=-\frac{\sqrt{210}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*15}=\frac{0+2\sqrt{210}}{30}
=\frac{2\sqrt{210}}{30}
=\frac{\sqrt{210}}{15}
$