(7x-5)(x+43)=0

Solution for (7x-5)(x+43)=0 equation:

(7x-5)(x+43)=0

We multiply parentheses ..

(+7x^2+301x-5x-215)=0

We get rid of parentheses

7x^2+301x-5x-215=0

We add all the numbers together, and all the variables

7x^2+296x-215=0

a = 7; b = 296; c = -215;
Δ = b2-4ac
Δ = 2962-4·7·(-215)
Δ = 93636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{93636}=306$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(296)-306}{2*7}=\frac{-602}{14}
=-43
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(296)+306}{2*7}=\frac{10}{14}
=5/7
$