2x^2-3=x^2+1-5x

Solution for 2x^2-3=x^2+1-5x equation:

2x^2-3=x^2+1-5x

We move all terms to the left:

2x^2-3-(x^2+1-5x)=0

We get rid of parentheses

2x^2-x^2+5x-1-3=0

We add all the numbers together, and all the variables

x^2+5x-4=0

a = 1; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·1·(-4)
Δ = 41
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{-(5)-\sqrt{41}}{2*1}=\frac{-5-\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{41}}{2*1}=\frac{-5+\sqrt{41}}{2}
$