3x2+152=4x2+11x

Solution for 3x2+152=4x2+11x equation:

3x^2+152=4x^2+11x

We move all terms to the left:

3x^2+152-(4x^2+11x)=0

We get rid of parentheses

3x^2-4x^2-11x+152=0

We add all the numbers together, and all the variables

-1x^2-11x+152=0

a = -1; b = -11; c = +152;
Δ = b2-4ac
Δ = -112-4·(-1)·152
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-27}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+27}{2*-1}=\frac{38}{-2}
=-19
$