3x+2=2x^2+7x-11

Solution for 3x+2=2x^2+7x-11 equation:

3x+2=2x^2+7x-11

We move all terms to the left:

3x+2-(2x^2+7x-11)=0

We get rid of parentheses

-2x^2+3x-7x+11+2=0

We add all the numbers together, and all the variables

-2x^2-4x+13=0

a = -2; b = -4; c = +13;
Δ = b2-4ac
Δ = -42-4·(-2)·13
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{30}}{2*-2}=\frac{4-2\sqrt{30}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{30}}{2*-2}=\frac{4+2\sqrt{30}}{-4}
$