-3/4x-X=-21

Solution for -3/4x-X=-21 equation:

-3/4x-x=-21

We move all terms to the left:

-3/4x-x-(-21)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x-3/4x+21=0

We multiply all the terms by the denominator


-1x*4x+21*4x-3=0

Wy multiply elements

-4x^2+84x-3=0

a = -4; b = 84; c = -3;
Δ = b2-4ac
Δ = 842-4·(-4)·(-3)
Δ = 7008
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:

$\sqrt{\Delta}=\sqrt{7008}=\sqrt{16*438}=\sqrt{16}*\sqrt{438}=4\sqrt{438}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{438}}{2*-4}=\frac{-84-4\sqrt{438}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{438}}{2*-4}=\frac{-84+4\sqrt{438}}{-8}
$