10x+3+3x=5x+1+8x2

Solution for 10x+3+3x=5x+1+8x2 equation:

10x+3+3x=5x+1+8x^2

We move all terms to the left:

10x+3+3x-(5x+1+8x^2)=0

We add all the numbers together, and all the variables

-(5x+1+8x^2)+13x+3=0

We get rid of parentheses

-8x^2-5x+13x-1+3=0

We add all the numbers together, and all the variables

-8x^2+8x+2=0

a = -8; b = 8; c = +2;
Δ = b2-4ac
Δ = 82-4·(-8)·2
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{2}}{2*-8}=\frac{-8-8\sqrt{2}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{2}}{2*-8}=\frac{-8+8\sqrt{2}}{-16}
$