5x2+x=9+3x+10

Solution for 5x2+x=9+3x+10 equation:

5x^2+x=9+3x+10

We move all terms to the left:

5x^2+x-(9+3x+10)=0

We add all the numbers together, and all the variables

5x^2+x-(3x+19)=0

We get rid of parentheses

5x^2+x-3x-19=0

We add all the numbers together, and all the variables

5x^2-2x-19=0

a = 5; b = -2; c = -19;
Δ = b2-4ac
Δ = -22-4·5·(-19)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8\sqrt{6}}{2*5}=\frac{2-8\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8\sqrt{6}}{2*5}=\frac{2+8\sqrt{6}}{10}
$