15x=-16x^2+45x

Solution for 15x=-16x^2+45x equation:

15x=-16x^2+45x

We move all terms to the left:

15x-(-16x^2+45x)=0

We get rid of parentheses

16x^2-45x+15x=0

We add all the numbers together, and all the variables

16x^2-30x=0

a = 16; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·16·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*16}=\frac{60}{32}
=1+7/8
$