10x2-37x+40=4x2-16

Solution for 10x2-37x+40=4x2-16 equation:

10x^2-37x+40=4x^2-16

We move all terms to the left:

10x^2-37x+40-(4x^2-16)=0

We get rid of parentheses

10x^2-4x^2-37x+16+40=0

We add all the numbers together, and all the variables

6x^2-37x+56=0

a = 6; b = -37; c = +56;
Δ = b2-4ac
Δ = -372-4·6·56
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{-(-37)-5}{2*6}=\frac{32}{12}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+5}{2*6}=\frac{42}{12}
=3+1/2
$