(-42x^2)+30x+30=(5x^2)+x+1

Solution for (-42x^2)+30x+30=(5x^2)+x+1 equation:

(-42x^2)+30x+30=(5x^2)+x+1

We move all terms to the left:

(-42x^2)+30x+30-((5x^2)+x+1)=0

We get rid of parentheses

-42x^2-5x^2+30x-x-1+30=0

We add all the numbers together, and all the variables

-47x^2+29x+29=0

a = -47; b = 29; c = +29;
Δ = b2-4ac
Δ = 292-4·(-47)·29
Δ = 6293
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{-(29)-\sqrt{6293}}{2*-47}=\frac{-29-\sqrt{6293}}{-94}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{6293}}{2*-47}=\frac{-29+\sqrt{6293}}{-94}
$