(2x-5)=(6x2-6x-11)

Solution for (2x-5)=(6x2-6x-11) equation:

(2x-5)=(6x^2-6x-11)

We move all terms to the left:

(2x-5)-((6x^2-6x-11))=0

We get rid of parentheses

2x-((6x^2-6x-11))-5=0


We calculate terms in parentheses: -((6x^2-6x-11)), so:

(6x^2-6x-11)

We get rid of parentheses

6x^2-6x-11

Back to the equation:

-(6x^2-6x-11)


We get rid of parentheses

-6x^2+2x+6x+11-5=0

We add all the numbers together, and all the variables

-6x^2+8x+6=0

a = -6; b = 8; c = +6;
Δ = b2-4ac
Δ = 82-4·(-6)·6
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{13}}{2*-6}=\frac{-8-4\sqrt{13}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{13}}{2*-6}=\frac{-8+4\sqrt{13}}{-12}
$