(7x-6)(3x-3)+(3x-11)(2x+3)=0

Solution for (7x-6)(3x-3)+(3x-11)(2x+3)=0 equation:

(7x-6)(3x-3)+(3x-11)(2x+3)=0

We multiply parentheses ..

(+21x^2-21x-18x+18)+(3x-11)(2x+3)=0

We get rid of parentheses

21x^2-21x-18x+(3x-11)(2x+3)+18=0

We multiply parentheses ..

21x^2+(+6x^2+9x-22x-33)-21x-18x+18=0

We add all the numbers together, and all the variables

21x^2+(+6x^2+9x-22x-33)-39x+18=0

We get rid of parentheses

21x^2+6x^2+9x-22x-39x-33+18=0

We add all the numbers together, and all the variables

27x^2-52x-15=0

a = 27; b = -52; c = -15;
Δ = b2-4ac
Δ = -522-4·27·(-15)
Δ = 4324
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:

$\sqrt{\Delta}=\sqrt{4324}=\sqrt{4*1081}=\sqrt{4}*\sqrt{1081}=2\sqrt{1081}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-2\sqrt{1081}}{2*27}=\frac{52-2\sqrt{1081}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+2\sqrt{1081}}{2*27}=\frac{52+2\sqrt{1081}}{54}
$