(30-x)(16-x)=46x-x2

Solution for (30-x)(16-x)=46x-x2 equation:

(30-x)(16-x)=46x-x2

We move all terms to the left:

(30-x)(16-x)-(46x-x2)=0

We add all the numbers together, and all the variables

-(+46x-1x^2)+(-1x+30)(-1x+16)=0

We get rid of parentheses

1x^2-46x+(-1x+30)(-1x+16)=0

We multiply parentheses ..

1x^2+(+x^2-16x-30x+480)-46x=0

We add all the numbers together, and all the variables

x^2+(+x^2-16x-30x+480)-46x=0

We get rid of parentheses

x^2+x^2-16x-30x-46x+480=0

We add all the numbers together, and all the variables

2x^2-92x+480=0

a = 2; b = -92; c = +480;
Δ = b2-4ac
Δ = -922-4·2·480
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-68}{2*2}=\frac{24}{4}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+68}{2*2}=\frac{160}{4}
=40
$