(6x^2)=5-5x

Solution for (6x^2)=5-5x equation:

(6x^2)=5-5x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

6x^2+5x-5=0

a = 6; b = 5; c = -5;
Δ = b2-4ac
Δ = 52-4·6·(-5)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{145}}{2*6}=\frac{-5-\sqrt{145}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{145}}{2*6}=\frac{-5+\sqrt{145}}{12}
$