6x^2=5-60x

Solution for 6x^2=5-60x equation:

6x^2=5-60x

We move all terms to the left:

6x^2-(5-60x)=0

We add all the numbers together, and all the variables

6x^2-(-60x+5)=0

We get rid of parentheses

6x^2+60x-5=0

a = 6; b = 60; c = -5;
Δ = b2-4ac
Δ = 602-4·6·(-5)
Δ = 3720
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:

$\sqrt{\Delta}=\sqrt{3720}=\sqrt{4*930}=\sqrt{4}*\sqrt{930}=2\sqrt{930}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{930}}{2*6}=\frac{-60-2\sqrt{930}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{930}}{2*6}=\frac{-60+2\sqrt{930}}{12}
$