7x^2=-2-15x

Solution for 7x^2=-2-15x equation:

7x^2=-2-15x

We move all terms to the left:

7x^2-(-2-15x)=0

We add all the numbers together, and all the variables

7x^2-(-15x-2)=0

We get rid of parentheses

7x^2+15x+2=0

a = 7; b = 15; c = +2;
Δ = b2-4ac
Δ = 152-4·7·2
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-13}{2*7}=\frac{-28}{14}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+13}{2*7}=\frac{-2}{14}
=-1/7
$