5x2=1-5x

Solution for 5x2=1-5x equation:

5x^2=1-5x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

5x^2+5x-1=0

a = 5; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·5·(-1)
Δ = 45
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{5}}{2*5}=\frac{-5-3\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{5}}{2*5}=\frac{-5+3\sqrt{5}}{10}
$