2x^2-3=-x+4

Solution for 2x^2-3=-x+4 equation:

2x^2-3=-x+4

We move all terms to the left:

2x^2-3-(-x+4)=0

We add all the numbers together, and all the variables

2x^2-(-1x+4)-3=0

We get rid of parentheses

2x^2+1x-4-3=0

We add all the numbers together, and all the variables

2x^2+x-7=0

a = 2; b = 1; c = -7;
Δ = b2-4ac
Δ = 12-4·2·(-7)
Δ = 57
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{-(1)-\sqrt{57}}{2*2}=\frac{-1-\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{57}}{2*2}=\frac{-1+\sqrt{57}}{4}
$