120-70x2/5=x

Solution for 120-70x2/5=x equation:

120-70x^2/5=x

We move all terms to the left:

120-70x^2/5-(x)=0

We add all the numbers together, and all the variables

-70x^2/5-1x+120=0

We multiply all the terms by the denominator


-70x^2-1x*5+120*5=0

We add all the numbers together, and all the variables

-70x^2-1x*5+600=0

Wy multiply elements

-70x^2-5x+600=0

a = -70; b = -5; c = +600;
Δ = b2-4ac
Δ = -52-4·(-70)·600
Δ = 168025
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:

$\sqrt{\Delta}=\sqrt{168025}=\sqrt{25*6721}=\sqrt{25}*\sqrt{6721}=5\sqrt{6721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{6721}}{2*-70}=\frac{5-5\sqrt{6721}}{-140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{6721}}{2*-70}=\frac{5+5\sqrt{6721}}{-140}
$