2b^2-12b+7=0

Solution for 2b^2-12b+7=0 equation:

2b^2-12b+7=0

a = 2; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·2·7
Δ = 88
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{22}}{2*2}=\frac{12-2\sqrt{22}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{22}}{2*2}=\frac{12+2\sqrt{22}}{4}
$