7x2/25=6

Solution for 7x2/25=6 equation:

7x^2/25=6

We move all terms to the left:

7x^2/25-(6)=0

We multiply all the terms by the denominator


7x^2-6*25=0

We add all the numbers together, and all the variables

7x^2-150=0

a = 7; b = 0; c = -150;
Δ = b2-4ac
Δ = 02-4·7·(-150)
Δ = 4200
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:

$\sqrt{\Delta}=\sqrt{4200}=\sqrt{100*42}=\sqrt{100}*\sqrt{42}=10\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{42}}{2*7}=\frac{0-10\sqrt{42}}{14}
=-\frac{10\sqrt{42}}{14}
=-\frac{5\sqrt{42}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{42}}{2*7}=\frac{0+10\sqrt{42}}{14}
=\frac{10\sqrt{42}}{14}
=\frac{5\sqrt{42}}{7}
$