(U-7)^2=2u^2-18u+37

Solution for (U-7)^2=2u^2-18u+37 equation:

(-7)^2=2U^2-18U+37

We move all terms to the left:

(-7)^2-(2U^2-18U+37)=0

We add all the numbers together, and all the variables

-(2U^2-18U+37)+49=0

We get rid of parentheses

-2U^2+18U-37+49=0

We add all the numbers together, and all the variables

-2U^2+18U+12=0

a = -2; b = 18; c = +12;
Δ = b2-4ac
Δ = 182-4·(-2)·12
Δ = 420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{105}}{2*-2}=\frac{-18-2\sqrt{105}}{-4}
$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{105}}{2*-2}=\frac{-18+2\sqrt{105}}{-4}
$