2x^2+11=3x+21

Solution for 2x^2+11=3x+21 equation:

2x^2+11=3x+21

We move all terms to the left:

2x^2+11-(3x+21)=0

We get rid of parentheses

2x^2-3x-21+11=0

We add all the numbers together, and all the variables

2x^2-3x-10=0

a = 2; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·2·(-10)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{89}}{2*2}=\frac{3-\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*2}=\frac{3+\sqrt{89}}{4}
$