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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

7x^2-21x+5x-20+5=0

We add all the numbers together, and all the variables

7x^2-16x-15=0

a = 7; b = -16; c = -15;
Δ = b2-4ac
Δ = -162-4·7·(-15)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-26}{2*7}=\frac{-10}{14}
=-5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+26}{2*7}=\frac{42}{14}
=3
$