(-41/4)x=-34

Solution for (-41/4)x=-34 equation:

(-41/4)x=-34

We move all terms to the left:

(-41/4)x-(-34)=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

(-41/4)x+34=0

We multiply parentheses

-41x^2+34=0

a = -41; b = 0; c = +34;
Δ = b2-4ac
Δ = 02-4·(-41)·34
Δ = 5576
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:

$\sqrt{\Delta}=\sqrt{5576}=\sqrt{4*1394}=\sqrt{4}*\sqrt{1394}=2\sqrt{1394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1394}}{2*-41}=\frac{0-2\sqrt{1394}}{-82}
=-\frac{2\sqrt{1394}}{-82}
=-\frac{\sqrt{1394}}{-41}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1394}}{2*-41}=\frac{0+2\sqrt{1394}}{-82}
=\frac{2\sqrt{1394}}{-82}
=\frac{\sqrt{1394}}{-41}
$