2x^2-4x+10=3x+14

Solution for 2x^2-4x+10=3x+14 equation:

2x^2-4x+10=3x+14

We move all terms to the left:

2x^2-4x+10-(3x+14)=0

We get rid of parentheses

2x^2-4x-3x-14+10=0

We add all the numbers together, and all the variables

2x^2-7x-4=0

a = 2; b = -7; c = -4;
Δ = b2-4ac
Δ = -72-4·2·(-4)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*2}=\frac{16}{4}
=4
$