21/4a-11=2a-15

Solution for 21/4a-11=2a-15 equation:

21/4a-11=2a-15

We move all terms to the left:

21/4a-11-(2a-15)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We get rid of parentheses

21/4a-2a+15-11=0

We multiply all the terms by the denominator


-2a*4a+15*4a-11*4a+21=0

Wy multiply elements

-8a^2+60a-44a+21=0

We add all the numbers together, and all the variables

-8a^2+16a+21=0

a = -8; b = 16; c = +21;
Δ = b2-4ac
Δ = 162-4·(-8)·21
Δ = 928
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{58}}{2*-8}=\frac{-16-4\sqrt{58}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{58}}{2*-8}=\frac{-16+4\sqrt{58}}{-16}
$