0=4x^2+5x+x^2-7

Solution for 0=4x^2+5x+x^2-7 equation:

0=4x^2+5x+x^2-7

We move all terms to the left:

0-(4x^2+5x+x^2-7)=0

We add all the numbers together, and all the variables

-(4x^2+5x+x^2-7)=0

We get rid of parentheses

-4x^2-x^2-5x+7=0

We add all the numbers together, and all the variables

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

a = -5; b = -5; c = +7;
Δ = b2-4ac
Δ = -52-4·(-5)·7
Δ = 165
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{-(-5)-\sqrt{165}}{2*-5}=\frac{5-\sqrt{165}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{165}}{2*-5}=\frac{5+\sqrt{165}}{-10}
$