5(6a+7)+2/3a-8=9

Solution for 5(6a+7)+2/3a-8=9 equation:

5(6a+7)+2/3a-8=9

We move all terms to the left:

5(6a+7)+2/3a-8-(9)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

5(6a+7)+2/3a-17=0

We multiply parentheses

30a+2/3a+35-17=0

We multiply all the terms by the denominator


30a*3a+35*3a-17*3a+2=0

Wy multiply elements

90a^2+105a-51a+2=0

We add all the numbers together, and all the variables

90a^2+54a+2=0

a = 90; b = 54; c = +2;
Δ = b2-4ac
Δ = 542-4·90·2
Δ = 2196
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:

$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{61}}{2*90}=\frac{-54-6\sqrt{61}}{180}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{61}}{2*90}=\frac{-54+6\sqrt{61}}{180}
$