(2x+7)(x-1)+(2x+7)(5x+4)=0

Solution for (2x+7)(x-1)+(2x+7)(5x+4)=0 equation:

(2x+7)(x-1)+(2x+7)(5x+4)=0

We multiply parentheses ..

(+2x^2-2x+7x-7)+(2x+7)(5x+4)=0

We get rid of parentheses

2x^2-2x+7x+(2x+7)(5x+4)-7=0

We multiply parentheses ..

2x^2+(+10x^2+8x+35x+28)-2x+7x-7=0

We add all the numbers together, and all the variables

2x^2+(+10x^2+8x+35x+28)+5x-7=0

We get rid of parentheses

2x^2+10x^2+8x+35x+5x+28-7=0

We add all the numbers together, and all the variables

12x^2+48x+21=0

a = 12; b = 48; c = +21;
Δ = b2-4ac
Δ = 482-4·12·21
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-36}{2*12}=\frac{-84}{24}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+36}{2*12}=\frac{-12}{24}
=-1/2
$