2x^2=12x-5

Solution for 2x^2=12x-5 equation:

2x^2=12x-5

We move all terms to the left:

2x^2-(12x-5)=0

We get rid of parentheses

2x^2-12x+5=0

a = 2; b = -12; c = +5;
Δ = b2-4ac
Δ = -122-4·2·5
Δ = 104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{26}}{2*2}=\frac{12-2\sqrt{26}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{26}}{2*2}=\frac{12+2\sqrt{26}}{4}
$