15x+5=18x^2+6

Solution for 15x+5=18x^2+6 equation:

15x+5=18x^2+6

We move all terms to the left:

15x+5-(18x^2+6)=0

We get rid of parentheses

-18x^2+15x-6+5=0

We add all the numbers together, and all the variables

-18x^2+15x-1=0

a = -18; b = 15; c = -1;
Δ = b2-4ac
Δ = 152-4·(-18)·(-1)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{17}}{2*-18}=\frac{-15-3\sqrt{17}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{17}}{2*-18}=\frac{-15+3\sqrt{17}}{-36}
$