(5x+7)(x+6)=0

Solution for (5x+7)(x+6)=0 equation:

(5x+7)(x+6)=0

We multiply parentheses ..

(+5x^2+30x+7x+42)=0

We get rid of parentheses

5x^2+30x+7x+42=0

We add all the numbers together, and all the variables

5x^2+37x+42=0

a = 5; b = 37; c = +42;
Δ = b2-4ac
Δ = 372-4·5·42
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-23}{2*5}=\frac{-60}{10}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+23}{2*5}=\frac{-14}{10}
=-1+2/5
$