5x^2-1=-7x

Solution for 5x^2-1=-7x equation:

5x^2-1=-7x

We move all terms to the left:

5x^2-1-(-7x)=0

We get rid of parentheses

5x^2+7x-1=0

a = 5; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·5·(-1)
Δ = 69
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{69}}{2*5}=\frac{-7-\sqrt{69}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{69}}{2*5}=\frac{-7+\sqrt{69}}{10}
$