0(x)=-16x^2+52x

Solution for 0(x)=-16x^2+52x equation:

0(x)=-16x^2+52x

We move all terms to the left:

0(x)-(-16x^2+52x)=0

We add all the numbers together, and all the variables

-(-16x^2+52x)+x=0

We get rid of parentheses

16x^2-52x+x=0

We add all the numbers together, and all the variables

16x^2-51x=0

a = 16; b = -51; c = 0;
Δ = b2-4ac
Δ = -512-4·16·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-51}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+51}{2*16}=\frac{102}{32}
=3+3/16
$