(U-7)^2=2u^2-10u+37

Solution for (U-7)^2=2u^2-10u+37 equation:

(-7)^2=2U^2-10U+37

We move all terms to the left:

(-7)^2-(2U^2-10U+37)=0

We add all the numbers together, and all the variables

-(2U^2-10U+37)+49=0

We get rid of parentheses

-2U^2+10U-37+49=0

We add all the numbers together, and all the variables

-2U^2+10U+12=0

a = -2; b = 10; c = +12;
Δ = b2-4ac
Δ = 102-4·(-2)·12
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*-2}=\frac{-24}{-4}
=+6
$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*-2}=\frac{4}{-4}
=-1
$