(7b+14)(3b+8)+(12b+5)(7b+14)=0

Solution for (7b+14)(3b+8)+(12b+5)(7b+14)=0 equation:

(7b+14)(3b+8)+(12b+5)(7b+14)=0

We multiply parentheses ..

(+21b^2+56b+42b+112)+(12b+5)(7b+14)=0

We get rid of parentheses

21b^2+56b+42b+(12b+5)(7b+14)+112=0

We multiply parentheses ..

21b^2+(+84b^2+168b+35b+70)+56b+42b+112=0

We add all the numbers together, and all the variables

21b^2+(+84b^2+168b+35b+70)+98b+112=0

We get rid of parentheses

21b^2+84b^2+168b+35b+98b+70+112=0

We add all the numbers together, and all the variables

105b^2+301b+182=0

a = 105; b = 301; c = +182;
Δ = b2-4ac
Δ = 3012-4·105·182
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(301)-119}{2*105}=\frac{-420}{210}
=-2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(301)+119}{2*105}=\frac{-182}{210}
=-13/15
$