2x^2-11=-4x+15

Solution for 2x^2-11=-4x+15 equation:

2x^2-11=-4x+15

We move all terms to the left:

2x^2-11-(-4x+15)=0

We get rid of parentheses

2x^2+4x-15-11=0

We add all the numbers together, and all the variables

2x^2+4x-26=0

a = 2; b = 4; c = -26;
Δ = b2-4ac
Δ = 42-4·2·(-26)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{14}}{2*2}=\frac{-4-4\sqrt{14}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{14}}{2*2}=\frac{-4+4\sqrt{14}}{4}
$