1=5x^2-40x+61

Solution for 1=5x^2-40x+61 equation:

1=5x^2-40x+61

We move all terms to the left:

1-(5x^2-40x+61)=0

We get rid of parentheses

-5x^2+40x-61+1=0

We add all the numbers together, and all the variables

-5x^2+40x-60=0

a = -5; b = 40; c = -60;
Δ = b2-4ac
Δ = 402-4·(-5)·(-60)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-20}{2*-5}=\frac{-60}{-10}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20}{2*-5}=\frac{-20}{-10}
=+2
$