x^2=6(x+5)

Solution for x^2=6(x+5) equation:

x^2=6(x+5)

We move all terms to the left:

x^2-(6(x+5))=0


We calculate terms in parentheses: -(6(x+5)), so:

6(x+5)

We multiply parentheses

6x+30

Back to the equation:

-(6x+30)


We get rid of parentheses

x^2-6x-30=0

a = 1; b = -6; c = -30;
Δ = b2-4ac
Δ = -62-4·1·(-30)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*1}=\frac{6-2\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*1}=\frac{6+2\sqrt{39}}{2}
$