-1/2=4x^2+6x-18

Solution for -1/2=4x^2+6x-18 equation:

-1/2=4x^2+6x-18

We move all terms to the left:

-1/2-(4x^2+6x-18)=0

We get rid of parentheses

-4x^2-6x+18-1/2=0

We multiply all the terms by the denominator


-4x^2*2-6x*2-1+18*2=0

We add all the numbers together, and all the variables

-4x^2*2-6x*2+35=0

Wy multiply elements

-8x^2-12x+35=0

a = -8; b = -12; c = +35;
Δ = b2-4ac
Δ = -122-4·(-8)·35
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{79}}{2*-8}=\frac{12-4\sqrt{79}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{79}}{2*-8}=\frac{12+4\sqrt{79}}{-16}
$