0=2x^2+7x-5

Solution for 0=2x^2+7x-5 equation:

0=2x^2+7x-5

We move all terms to the left:

0-(2x^2+7x-5)=0

We add all the numbers together, and all the variables

-(2x^2+7x-5)=0

We get rid of parentheses

-2x^2-7x+5=0

a = -2; b = -7; c = +5;
Δ = b2-4ac
Δ = -72-4·(-2)·5
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{89}}{2*-2}=\frac{7-\sqrt{89}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{89}}{2*-2}=\frac{7+\sqrt{89}}{-4}
$