18x^2-39x-7=(6x+1)

Solution for 18x^2-39x-7=(6x+1) equation:

18x^2-39x-7=(6x+1)

We move all terms to the left:

18x^2-39x-7-((6x+1))=0


We calculate terms in parentheses: -((6x+1)), so:

(6x+1)

We get rid of parentheses

6x+1

Back to the equation:

-(6x+1)


We get rid of parentheses

18x^2-39x-6x-1-7=0

We add all the numbers together, and all the variables

18x^2-45x-8=0

a = 18; b = -45; c = -8;
Δ = b2-4ac
Δ = -452-4·18·(-8)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-51}{2*18}=\frac{-6}{36}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+51}{2*18}=\frac{96}{36}
=2+2/3
$