(4x+7)(3x+5)=0

Solution for (4x+7)(3x+5)=0 equation:

(4x+7)(3x+5)=0

We multiply parentheses ..

(+12x^2+20x+21x+35)=0

We get rid of parentheses

12x^2+20x+21x+35=0

We add all the numbers together, and all the variables

12x^2+41x+35=0

a = 12; b = 41; c = +35;
Δ = b2-4ac
Δ = 412-4·12·35
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-1}{2*12}=\frac{-42}{24}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+1}{2*12}=\frac{-40}{24}
=-1+2/3
$