(8+14)(14)=(5+x)(x)

Solution for (8+14)(14)=(5+x)(x) equation:

(8+14)(14)=(5+x)(x)

We move all terms to the left:

(8+14)(14)-((5+x)(x))=0

We add all the numbers together, and all the variables

-((x+5)x)+2214=0


We calculate terms in parentheses: -((x+5)x), so:

(x+5)x

We multiply parentheses

x^2+5x

Back to the equation:

-(x^2+5x)


We get rid of parentheses

-x^2-5x+2214=0

We add all the numbers together, and all the variables

-1x^2-5x+2214=0

a = -1; b = -5; c = +2214;
Δ = b2-4ac
Δ = -52-4·(-1)·2214
Δ = 8881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{8881}}{2*-1}=\frac{5-\sqrt{8881}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{8881}}{2*-1}=\frac{5+\sqrt{8881}}{-2}
$