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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

35x^2+62x+24=0

a = 35; b = 62; c = +24;
Δ = b2-4ac
Δ = 622-4·35·24
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-22}{2*35}=\frac{-84}{70}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+22}{2*35}=\frac{-40}{70}
=-4/7
$