X=4x^2-5x-6-4x+3

Solution for X=4x^2-5x-6-4x+3 equation:

X=4X^2-5X-6-4X+3

We move all terms to the left:

X-(4X^2-5X-6-4X+3)=0

We get rid of parentheses

-4X^2+X+5X+4X+6-3=0

We add all the numbers together, and all the variables

-4X^2+10X+3=0

a = -4; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·(-4)·3
Δ = 148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{37}}{2*-4}=\frac{-10-2\sqrt{37}}{-8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{37}}{2*-4}=\frac{-10+2\sqrt{37}}{-8}
$