2x^2-16x=4x^2-3x-7

Solution for 2x^2-16x=4x^2-3x-7 equation:

2x^2-16x=4x^2-3x-7

We move all terms to the left:

2x^2-16x-(4x^2-3x-7)=0

We get rid of parentheses

2x^2-4x^2-16x+3x+7=0

We add all the numbers together, and all the variables

-2x^2-13x+7=0

a = -2; b = -13; c = +7;
Δ = b2-4ac
Δ = -132-4·(-2)·7
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-15}{2*-2}=\frac{-2}{-4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+15}{2*-2}=\frac{28}{-4}
=-7
$