5x+10=4x^2-215

Solution for 5x+10=4x^2-215 equation:

5x+10=4x^2-215

We move all terms to the left:

5x+10-(4x^2-215)=0

We get rid of parentheses

-4x^2+5x+215+10=0

We add all the numbers together, and all the variables

-4x^2+5x+225=0

a = -4; b = 5; c = +225;
Δ = b2-4ac
Δ = 52-4·(-4)·225
Δ = 3625
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:

$\sqrt{\Delta}=\sqrt{3625}=\sqrt{25*145}=\sqrt{25}*\sqrt{145}=5\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{145}}{2*-4}=\frac{-5-5\sqrt{145}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{145}}{2*-4}=\frac{-5+5\sqrt{145}}{-8}
$