(3x+5)(4x+1)=-5

Solution for (3x+5)(4x+1)=-5 equation:

(3x+5)(4x+1)=-5

We move all terms to the left:

(3x+5)(4x+1)-(-5)=0

We add all the numbers together, and all the variables

(3x+5)(4x+1)+5=0

We multiply parentheses ..

(+12x^2+3x+20x+5)+5=0

We get rid of parentheses

12x^2+3x+20x+5+5=0

We add all the numbers together, and all the variables

12x^2+23x+10=0

a = 12; b = 23; c = +10;
Δ = b2-4ac
Δ = 232-4·12·10
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-7}{2*12}=\frac{-30}{24}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+7}{2*12}=\frac{-16}{24}
=-2/3
$