(12x+7)(4x+10)+(9x+8)(12x+7)=0

Solution for (12x+7)(4x+10)+(9x+8)(12x+7)=0 equation:

(12x+7)(4x+10)+(9x+8)(12x+7)=0

We multiply parentheses ..

(+48x^2+120x+28x+70)+(9x+8)(12x+7)=0

We get rid of parentheses

48x^2+120x+28x+(9x+8)(12x+7)+70=0

We multiply parentheses ..

48x^2+(+108x^2+63x+96x+56)+120x+28x+70=0

We add all the numbers together, and all the variables

48x^2+(+108x^2+63x+96x+56)+148x+70=0

We get rid of parentheses

48x^2+108x^2+63x+96x+148x+56+70=0

We add all the numbers together, and all the variables

156x^2+307x+126=0

a = 156; b = 307; c = +126;
Δ = b2-4ac
Δ = 3072-4·156·126
Δ = 15625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15625}=125$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(307)-125}{2*156}=\frac{-432}{312}
=-1+5/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(307)+125}{2*156}=\frac{-182}{312}
=-7/12
$