6x2-3x+5=x+25+11

Solution for 6x2-3x+5=x+25+11 equation:

6x^2-3x+5=x+25+11

We move all terms to the left:

6x^2-3x+5-(x+25+11)=0

We add all the numbers together, and all the variables

6x^2-3x-(x+36)+5=0

We get rid of parentheses

6x^2-3x-x-36+5=0

We add all the numbers together, and all the variables

6x^2-4x-31=0

a = 6; b = -4; c = -31;
Δ = b2-4ac
Δ = -42-4·6·(-31)
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{190}}{2*6}=\frac{4-2\sqrt{190}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{190}}{2*6}=\frac{4+2\sqrt{190}}{12}
$