0.15625x^2+5x=40

Solution for 0.15625x^2+5x=40 equation:

0.15625x^2+5x=40

We move all terms to the left:

0.15625x^2+5x-(40)=0

a = 0.15625; b = 5; c = -40;
Δ = b2-4ac
Δ = 52-4·0.15625·(-40)
Δ = 50
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:

$\sqrt{\Delta}=\sqrt{50}=\sqrt{25*2}=\sqrt{25}*\sqrt{2}=5\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{2}}{2*0.15625}=\frac{-5-5\sqrt{2}}{0.3125}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{2}}{2*0.15625}=\frac{-5+5\sqrt{2}}{0.3125}
$