4X+9=3x*3x-18

Solution for 4X+9=3x*3x-18 equation:

4X+9=3X*3X-18

We move all terms to the left:

4X+9-(3X*3X-18)=0

We get rid of parentheses

4X-3X*3X+18+9=0

We add all the numbers together, and all the variables

4X-3X*3X+27=0

Wy multiply elements

-9X^2+4X+27=0

a = -9; b = 4; c = +27;
Δ = b2-4ac
Δ = 42-4·(-9)·27
Δ = 988
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:

$\sqrt{\Delta}=\sqrt{988}=\sqrt{4*247}=\sqrt{4}*\sqrt{247}=2\sqrt{247}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{247}}{2*-9}=\frac{-4-2\sqrt{247}}{-18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{247}}{2*-9}=\frac{-4+2\sqrt{247}}{-18}
$