21=3x+8/4x-7

Solution for 21=3x+8/4x-7 equation:

21=3x+8/4x-7

We move all terms to the left:

21-(3x+8/4x-7)=0


Domain of the equation: 4x-7)!=0

x∈R


We get rid of parentheses

-3x-8/4x+7+21=0

We multiply all the terms by the denominator


-3x*4x+7*4x+21*4x-8=0

Wy multiply elements

-12x^2+28x+84x-8=0

We add all the numbers together, and all the variables

-12x^2+112x-8=0

a = -12; b = 112; c = -8;
Δ = b2-4ac
Δ = 1122-4·(-12)·(-8)
Δ = 12160
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:

$\sqrt{\Delta}=\sqrt{12160}=\sqrt{64*190}=\sqrt{64}*\sqrt{190}=8\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-8\sqrt{190}}{2*-12}=\frac{-112-8\sqrt{190}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+8\sqrt{190}}{2*-12}=\frac{-112+8\sqrt{190}}{-24}
$