4x^2-33x+37=-9x+10

Solution for 4x^2-33x+37=-9x+10 equation:

4x^2-33x+37=-9x+10

We move all terms to the left:

4x^2-33x+37-(-9x+10)=0

We get rid of parentheses

4x^2-33x+9x-10+37=0

We add all the numbers together, and all the variables

4x^2-24x+27=0

a = 4; b = -24; c = +27;
Δ = b2-4ac
Δ = -242-4·4·27
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12}{2*4}=\frac{12}{8}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12}{2*4}=\frac{36}{8}
=4+1/2
$