14(14+16)=x(x+23)

Solution for 14(14+16)=x(x+23) equation:

14(14+16)=x(x+23)

We move all terms to the left:

14(14+16)-(x(x+23))=0

We add all the numbers together, and all the variables

-(x(x+23))+1430=0


We calculate terms in parentheses: -(x(x+23)), so:

x(x+23)

We multiply parentheses

x^2+23x

Back to the equation:

-(x^2+23x)


We get rid of parentheses

-x^2-23x+1430=0

We add all the numbers together, and all the variables

-1x^2-23x+1430=0

a = -1; b = -23; c = +1430;
Δ = b2-4ac
Δ = -232-4·(-1)·1430
Δ = 6249
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{-(-23)-\sqrt{6249}}{2*-1}=\frac{23-\sqrt{6249}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{6249}}{2*-1}=\frac{23+\sqrt{6249}}{-2}
$