2x^2-5x+7=3x^2+1

Solution for 2x^2-5x+7=3x^2+1 equation:

2x^2-5x+7=3x^2+1

We move all terms to the left:

2x^2-5x+7-(3x^2+1)=0

We get rid of parentheses

2x^2-3x^2-5x-1+7=0

We add all the numbers together, and all the variables

-1x^2-5x+6=0

a = -1; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·(-1)·6
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*-1}=\frac{12}{-2}
=-6
$