6x^2-175+x^2=8(x^2-50)

Solution for 6x^2-175+x^2=8(x^2-50) equation:

6x^2-175+x^2=8(x^2-50)

We move all terms to the left:

6x^2-175+x^2-(8(x^2-50))=0

We add all the numbers together, and all the variables

7x^2-(8(x^2-50))-175=0


We calculate terms in parentheses: -(8(x^2-50)), so:

8(x^2-50)

We multiply parentheses

8x^2-400

Back to the equation:

-(8x^2-400)


We get rid of parentheses

7x^2-8x^2+400-175=0

We add all the numbers together, and all the variables

-1x^2+225=0

a = -1; b = 0; c = +225;
Δ = b2-4ac
Δ = 02-4·(-1)·225
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*-1}=\frac{-30}{-2}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*-1}=\frac{30}{-2}
=-15
$