6x^2-42x+66=10x^2-80x+150

Solution for 6x^2-42x+66=10x^2-80x+150 equation:

6x^2-42x+66=10x^2-80x+150

We move all terms to the left:

6x^2-42x+66-(10x^2-80x+150)=0

We get rid of parentheses

6x^2-10x^2-42x+80x-150+66=0

We add all the numbers together, and all the variables

-4x^2+38x-84=0

a = -4; b = 38; c = -84;
Δ = b2-4ac
Δ = 382-4·(-4)·(-84)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-10}{2*-4}=\frac{-48}{-8}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+10}{2*-4}=\frac{-28}{-8}
=3+1/2
$