4x2-15x+37=9x+2

Solution for 4x2-15x+37=9x+2 equation:

4x^2-15x+37=9x+2

We move all terms to the left:

4x^2-15x+37-(9x+2)=0

We get rid of parentheses

4x^2-15x-9x-2+37=0

We add all the numbers together, and all the variables

4x^2-24x+35=0

a = 4; b = -24; c = +35;
Δ = b2-4ac
Δ = -242-4·4·35
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4}{2*4}=\frac{20}{8}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4}{2*4}=\frac{28}{8}
=3+1/2
$