-1=-x(5x+3)

Solution for -1=-x(5x+3) equation:

-1=-x(5x+3)

We move all terms to the left:

-1-(-x(5x+3))=0


We calculate terms in parentheses: -(-x(5x+3)), so:

-x(5x+3)

We multiply parentheses

-5x^2-3x

Back to the equation:

-(-5x^2-3x)


We get rid of parentheses

5x^2+3x-1=0

a = 5; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·5·(-1)
Δ = 29
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{-(3)-\sqrt{29}}{2*5}=\frac{-3-\sqrt{29}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{29}}{2*5}=\frac{-3+\sqrt{29}}{10}
$