(7x+4)(6x+5)=0

Solution for (7x+4)(6x+5)=0 equation:

(7x+4)(6x+5)=0

We multiply parentheses ..

(+42x^2+35x+24x+20)=0

We get rid of parentheses

42x^2+35x+24x+20=0

We add all the numbers together, and all the variables

42x^2+59x+20=0

a = 42; b = 59; c = +20;
Δ = b2-4ac
Δ = 592-4·42·20
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-11}{2*42}=\frac{-70}{84}
=-5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+11}{2*42}=\frac{-48}{84}
=-4/7
$