5x^2-11x+120=44x-30

Solution for 5x^2-11x+120=44x-30 equation:

5x^2-11x+120=44x-30

We move all terms to the left:

5x^2-11x+120-(44x-30)=0

We get rid of parentheses

5x^2-11x-44x+30+120=0

We add all the numbers together, and all the variables

5x^2-55x+150=0

a = 5; b = -55; c = +150;
Δ = b2-4ac
Δ = -552-4·5·150
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5}{2*5}=\frac{50}{10}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5}{2*5}=\frac{60}{10}
=6
$