3x+11=6x2-10

Solution for 3x+11=6x2-10 equation:

3x+11=6x^2-10

We move all terms to the left:

3x+11-(6x^2-10)=0

We get rid of parentheses

-6x^2+3x+10+11=0

We add all the numbers together, and all the variables

-6x^2+3x+21=0

a = -6; b = 3; c = +21;
Δ = b2-4ac
Δ = 32-4·(-6)·21
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{57}}{2*-6}=\frac{-3-3\sqrt{57}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{57}}{2*-6}=\frac{-3+3\sqrt{57}}{-12}
$