(7/4)(x)-9=7

Solution for (7/4)(x)-9=7 equation:

(7/4)(x)-9=7

We move all terms to the left:

(7/4)(x)-9-(7)=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

(+7/4)x-9-7=0

We add all the numbers together, and all the variables

(+7/4)x-16=0

We multiply parentheses

7x^2-16=0

a = 7; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·7·(-16)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{7}}{2*7}=\frac{0-8\sqrt{7}}{14}
=-\frac{8\sqrt{7}}{14}
=-\frac{4\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7}}{2*7}=\frac{0+8\sqrt{7}}{14}
=\frac{8\sqrt{7}}{14}
=\frac{4\sqrt{7}}{7}
$