8x^2+3x=3x^2+18x+18

Solution for 8x^2+3x=3x^2+18x+18 equation:

8x^2+3x=3x^2+18x+18

We move all terms to the left:

8x^2+3x-(3x^2+18x+18)=0

We get rid of parentheses

8x^2-3x^2+3x-18x-18=0

We add all the numbers together, and all the variables

5x^2-15x-18=0

a = 5; b = -15; c = -18;
Δ = b2-4ac
Δ = -152-4·5·(-18)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{65}}{2*5}=\frac{15-3\sqrt{65}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{65}}{2*5}=\frac{15+3\sqrt{65}}{10}
$