0=4x^2-7x-10

Solution for 0=4x^2-7x-10 equation:

0=4x^2-7x-10

We move all terms to the left:

0-(4x^2-7x-10)=0

We add all the numbers together, and all the variables

-(4x^2-7x-10)=0

We get rid of parentheses

-4x^2+7x+10=0

a = -4; b = 7; c = +10;
Δ = b2-4ac
Δ = 72-4·(-4)·10
Δ = 209
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{209}}{2*-4}=\frac{-7-\sqrt{209}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{209}}{2*-4}=\frac{-7+\sqrt{209}}{-8}
$