0=(x^2-6x)-50(x^2-6x)-275

Solution for 0=(x^2-6x)-50(x^2-6x)-275 equation:

0=(x^2-6x)-50(x^2-6x)-275

We move all terms to the left:

0-((x^2-6x)-50(x^2-6x)-275)=0

We add all the numbers together, and all the variables

-((x^2-6x)-50(x^2-6x)-275)=0


We calculate terms in parentheses: -((x^2-6x)-50(x^2-6x)-275), so:

(x^2-6x)-50(x^2-6x)-275

We multiply parentheses

-50x^2+(x^2-6x)+300x-275

We get rid of parentheses

-50x^2+x^2-6x+300x-275

We add all the numbers together, and all the variables

-49x^2+294x-275

Back to the equation:

-(-49x^2+294x-275)


We get rid of parentheses

49x^2-294x+275=0

a = 49; b = -294; c = +275;
Δ = b2-4ac
Δ = -2942-4·49·275
Δ = 32536
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:

$\sqrt{\Delta}=\sqrt{32536}=\sqrt{196*166}=\sqrt{196}*\sqrt{166}=14\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-294)-14\sqrt{166}}{2*49}=\frac{294-14\sqrt{166}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-294)+14\sqrt{166}}{2*49}=\frac{294+14\sqrt{166}}{98}
$