2x+21=3/4x-4

Solution for 2x+21=3/4x-4 equation:

2x+21=3/4x-4

We move all terms to the left:

2x+21-(3/4x-4)=0


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

x∈R


We get rid of parentheses

2x-3/4x+4+21=0

We multiply all the terms by the denominator


2x*4x+4*4x+21*4x-3=0

Wy multiply elements

8x^2+16x+84x-3=0

We add all the numbers together, and all the variables

8x^2+100x-3=0

a = 8; b = 100; c = -3;
Δ = b2-4ac
Δ = 1002-4·8·(-3)
Δ = 10096
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:

$\sqrt{\Delta}=\sqrt{10096}=\sqrt{16*631}=\sqrt{16}*\sqrt{631}=4\sqrt{631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{631}}{2*8}=\frac{-100-4\sqrt{631}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{631}}{2*8}=\frac{-100+4\sqrt{631}}{16}
$