x^2+8x+6=16/9

Solution for x^2+8x+6=16/9 equation:

x^2+8x+6=16/9

We move all terms to the left:

x^2+8x+6-(16/9)=0

We add all the numbers together, and all the variables

x^2+8x+6-(+16/9)=0

We get rid of parentheses

x^2+8x+6-16/9=0

We multiply all the terms by the denominator


x^2*9+8x*9-16+6*9=0

We add all the numbers together, and all the variables

x^2*9+8x*9+38=0

Wy multiply elements

9x^2+72x+38=0

a = 9; b = 72; c = +38;
Δ = b2-4ac
Δ = 722-4·9·38
Δ = 3816
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:

$\sqrt{\Delta}=\sqrt{3816}=\sqrt{36*106}=\sqrt{36}*\sqrt{106}=6\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-6\sqrt{106}}{2*9}=\frac{-72-6\sqrt{106}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+6\sqrt{106}}{2*9}=\frac{-72+6\sqrt{106}}{18}
$