0=2x^2-10x+7

Solution for 0=2x^2-10x+7 equation:

0=2x^2-10x+7

We move all terms to the left:

0-(2x^2-10x+7)=0

We add all the numbers together, and all the variables

-(2x^2-10x+7)=0

We get rid of parentheses

-2x^2+10x-7=0

a = -2; b = 10; c = -7;
Δ = b2-4ac
Δ = 102-4·(-2)·(-7)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{11}}{2*-2}=\frac{-10-2\sqrt{11}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{11}}{2*-2}=\frac{-10+2\sqrt{11}}{-4}
$