3x^2-7x=x^2-14x-4

Solution for 3x^2-7x=x^2-14x-4 equation:

3x^2-7x=x^2-14x-4

We move all terms to the left:

3x^2-7x-(x^2-14x-4)=0

We get rid of parentheses

3x^2-x^2-7x+14x+4=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 = 17
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{-(7)-\sqrt{17}}{2*2}=\frac{-7-\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{17}}{2*2}=\frac{-7+\sqrt{17}}{4}
$