X=(5x2)+1/2(10)(4)

Solution for X=(5x2)+1/2(10)(4) equation:

X=(5X^2)+1/2(10)(4)

We move all terms to the left:

X-((5X^2)+1/2(10)(4))=0

We get rid of parentheses

-5X^2+X-1/2104=0

We multiply all the terms by the denominator


-5X^2*2104+X*2104-1=0

Wy multiply elements

-10520X^2+2104X-1=0

a = -10520; b = 2104; c = -1;
Δ = b2-4ac
Δ = 21042-4·(-10520)·(-1)
Δ = 4384736
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:

$\sqrt{\Delta}=\sqrt{4384736}=\sqrt{16*274046}=\sqrt{16}*\sqrt{274046}=4\sqrt{274046}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2104)-4\sqrt{274046}}{2*-10520}=\frac{-2104-4\sqrt{274046}}{-21040}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2104)+4\sqrt{274046}}{2*-10520}=\frac{-2104+4\sqrt{274046}}{-21040}
$