4x(2x-20)=263-6x

Solution for 4x(2x-20)=263-6x equation:

4x(2x-20)=263-6x

We move all terms to the left:

4x(2x-20)-(263-6x)=0

We add all the numbers together, and all the variables

4x(2x-20)-(-6x+263)=0

We multiply parentheses

8x^2-80x-(-6x+263)=0

We get rid of parentheses

8x^2-80x+6x-263=0

We add all the numbers together, and all the variables

8x^2-74x-263=0

a = 8; b = -74; c = -263;
Δ = b2-4ac
Δ = -742-4·8·(-263)
Δ = 13892
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:

$\sqrt{\Delta}=\sqrt{13892}=\sqrt{4*3473}=\sqrt{4}*\sqrt{3473}=2\sqrt{3473}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{3473}}{2*8}=\frac{74-2\sqrt{3473}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{3473}}{2*8}=\frac{74+2\sqrt{3473}}{16}
$