x=7x^2-6x-18

Solution for x=7x^2-6x-18 equation:

x=7x^2-6x-18

We move all terms to the left:

x-(7x^2-6x-18)=0

We get rid of parentheses

-7x^2+x+6x+18=0

We add all the numbers together, and all the variables

-7x^2+7x+18=0

a = -7; b = 7; c = +18;
Δ = b2-4ac
Δ = 72-4·(-7)·18
Δ = 553
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{553}}{2*-7}=\frac{-7-\sqrt{553}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{553}}{2*-7}=\frac{-7+\sqrt{553}}{-14}
$