-4/7a-5=3a+8

Solution for -4/7a-5=3a+8 equation:

-4/7a-5=3a+8

We move all terms to the left:

-4/7a-5-(3a+8)=0


Domain of the equation: 7a!=0

a!=0/7

a!=0

a∈R


We get rid of parentheses

-4/7a-3a-8-5=0

We multiply all the terms by the denominator


-3a*7a-8*7a-5*7a-4=0

Wy multiply elements

-21a^2-56a-35a-4=0

We add all the numbers together, and all the variables

-21a^2-91a-4=0

a = -21; b = -91; c = -4;
Δ = b2-4ac
Δ = -912-4·(-21)·(-4)
Δ = 7945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-\sqrt{7945}}{2*-21}=\frac{91-\sqrt{7945}}{-42}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+\sqrt{7945}}{2*-21}=\frac{91+\sqrt{7945}}{-42}
$