10x^2-5x-25=5x

Solution for 10x^2-5x-25=5x equation:

10x^2-5x-25=5x

We move all terms to the left:

10x^2-5x-25-(5x)=0

We add all the numbers together, and all the variables

10x^2-10x-25=0

a = 10; b = -10; c = -25;
Δ = b2-4ac
Δ = -102-4·10·(-25)
Δ = 1100
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:

$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{11}}{2*10}=\frac{10-10\sqrt{11}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{11}}{2*10}=\frac{10+10\sqrt{11}}{20}
$