5x^2-40x=61

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

5x^2-40x=61

We move all terms to the left:

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

a = 5; b = -40; c = -61;
Δ = b2-4ac
Δ = -402-4·5·(-61)
Δ = 2820
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:

$\sqrt{\Delta}=\sqrt{2820}=\sqrt{4*705}=\sqrt{4}*\sqrt{705}=2\sqrt{705}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{705}}{2*5}=\frac{40-2\sqrt{705}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{705}}{2*5}=\frac{40+2\sqrt{705}}{10}
$