(6x+50)=(x^2+10)

Solution for (6x+50)=(x^2+10) equation:

(6x+50)=(x^2+10)

We move all terms to the left:

(6x+50)-((x^2+10))=0

We get rid of parentheses

6x-((x^2+10))+50=0


We calculate terms in parentheses: -((x^2+10)), so:

(x^2+10)

We get rid of parentheses

x^2+10

Back to the equation:

-(x^2+10)


We get rid of parentheses

-x^2+6x-10+50=0

We add all the numbers together, and all the variables

-1x^2+6x+40=0

a = -1; b = 6; c = +40;
Δ = b2-4ac
Δ = 62-4·(-1)·40
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*-1}=\frac{8}{-2}
=-4
$