7x2+12x=-5

Solution for 7x2+12x=-5 equation:

7x^2+12x=-5

We move all terms to the left:

7x^2+12x-(-5)=0

We add all the numbers together, and all the variables

7x^2+12x+5=0

a = 7; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·7·5
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2}{2*7}=\frac{-14}{14}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2}{2*7}=\frac{-10}{14}
=-5/7
$