2x^2+x=10+5x

Solution for 2x^2+x=10+5x equation:

2x^2+x=10+5x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

2x^2+x-5x-10=0

We add all the numbers together, and all the variables

2x^2-4x-10=0

a = 2; b = -4; c = -10;
Δ = b2-4ac
Δ = -42-4·2·(-10)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{6}}{2*2}=\frac{4-4\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{6}}{2*2}=\frac{4+4\sqrt{6}}{4}
$