30x^2+45+15=40x^2-22x-6

Solution for 30x^2+45+15=40x^2-22x-6 equation:

30x^2+45+15=40x^2-22x-6

We move all terms to the left:

30x^2+45+15-(40x^2-22x-6)=0

We add all the numbers together, and all the variables

30x^2-(40x^2-22x-6)+60=0

We get rid of parentheses

30x^2-40x^2+22x+6+60=0

We add all the numbers together, and all the variables

-10x^2+22x+66=0

a = -10; b = 22; c = +66;
Δ = b2-4ac
Δ = 222-4·(-10)·66
Δ = 3124
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:

$\sqrt{\Delta}=\sqrt{3124}=\sqrt{4*781}=\sqrt{4}*\sqrt{781}=2\sqrt{781}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{781}}{2*-10}=\frac{-22-2\sqrt{781}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{781}}{2*-10}=\frac{-22+2\sqrt{781}}{-20}
$