(3x+11)(13x+2)+(8x+4)(3x+11)=0

Solution for (3x+11)(13x+2)+(8x+4)(3x+11)=0 equation:

(3x+11)(13x+2)+(8x+4)(3x+11)=0

We multiply parentheses ..

(+39x^2+6x+143x+22)+(8x+4)(3x+11)=0

We get rid of parentheses

39x^2+6x+143x+(8x+4)(3x+11)+22=0

We multiply parentheses ..

39x^2+(+24x^2+88x+12x+44)+6x+143x+22=0

We add all the numbers together, and all the variables

39x^2+(+24x^2+88x+12x+44)+149x+22=0

We get rid of parentheses

39x^2+24x^2+88x+12x+149x+44+22=0

We add all the numbers together, and all the variables

63x^2+249x+66=0

a = 63; b = 249; c = +66;
Δ = b2-4ac
Δ = 2492-4·63·66
Δ = 45369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{45369}=213$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(249)-213}{2*63}=\frac{-462}{126}
=-3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(249)+213}{2*63}=\frac{-36}{126}
=-2/7
$