(43/4)*x=7

Solution for (43/4)*x=7 equation:

(43/4)*x=7

We move all terms to the left:

(43/4)*x-(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

(+43/4)*x-7=0

We multiply parentheses

43x^2-7=0

a = 43; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·43·(-7)
Δ = 1204
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:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{301}}{2*43}=\frac{0-2\sqrt{301}}{86}
=-\frac{2\sqrt{301}}{86}
=-\frac{\sqrt{301}}{43}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{301}}{2*43}=\frac{0+2\sqrt{301}}{86}
=\frac{2\sqrt{301}}{86}
=\frac{\sqrt{301}}{43}
$