X+2x2-4=-7x+6

Solution for X+2x2-4=-7x+6 equation:

X+2X^2-4=-7X+6

We move all terms to the left:

X+2X^2-4-(-7X+6)=0

We get rid of parentheses

2X^2+X+7X-6-4=0

We add all the numbers together, and all the variables

2X^2+8X-10=0

a = 2; b = 8; c = -10;
Δ = b2-4ac
Δ = 82-4·2·(-10)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12}{2*2}=\frac{-20}{4}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12}{2*2}=\frac{4}{4}
=1
$