4x(x-2)=x+10

Solution for 4x(x-2)=x+10 equation:

4x(x-2)=x+10

We move all terms to the left:

4x(x-2)-(x+10)=0

We multiply parentheses

4x^2-8x-(x+10)=0

We get rid of parentheses

4x^2-8x-x-10=0

We add all the numbers together, and all the variables

4x^2-9x-10=0

a = 4; b = -9; c = -10;
Δ = b2-4ac
Δ = -92-4·4·(-10)
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{241}}{2*4}=\frac{9-\sqrt{241}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{241}}{2*4}=\frac{9+\sqrt{241}}{8}
$