6x+5=9x^2-4

Solution for 6x+5=9x^2-4 equation:

6x+5=9x^2-4

We move all terms to the left:

6x+5-(9x^2-4)=0

We get rid of parentheses

-9x^2+6x+4+5=0

We add all the numbers together, and all the variables

-9x^2+6x+9=0

a = -9; b = 6; c = +9;
Δ = b2-4ac
Δ = 62-4·(-9)·9
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{10}}{2*-9}=\frac{-6-6\sqrt{10}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{10}}{2*-9}=\frac{-6+6\sqrt{10}}{-18}
$