X=(-16x^2)+30x+4

Solution for X=(-16x^2)+30x+4 equation:

X=(-16X^2)+30X+4

We move all terms to the left:

X-((-16X^2)+30X+4)=0


We calculate terms in parentheses: -((-16X^2)+30X+4), so:

(-16X^2)+30X+4

We get rid of parentheses

-16X^2+30X+4

Back to the equation:

-(-16X^2+30X+4)


We get rid of parentheses

16X^2-30X+X-4=0

We add all the numbers together, and all the variables

16X^2-29X-4=0

a = 16; b = -29; c = -4;
Δ = b2-4ac
Δ = -292-4·16·(-4)
Δ = 1097
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{-(-29)-\sqrt{1097}}{2*16}=\frac{29-\sqrt{1097}}{32}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{1097}}{2*16}=\frac{29+\sqrt{1097}}{32}
$