x2-5=-4x2+3x

Solution for x2-5=-4x2+3x equation:

x2-5=-4x^2+3x

We move all terms to the left:

x2-5-(-4x^2+3x)=0

We add all the numbers together, and all the variables

x^2-(-4x^2+3x)-5=0

We get rid of parentheses

x^2+4x^2-3x-5=0

We add all the numbers together, and all the variables

5x^2-3x-5=0

a = 5; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·5·(-5)
Δ = 109
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{-(-3)-\sqrt{109}}{2*5}=\frac{3-\sqrt{109}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{109}}{2*5}=\frac{3+\sqrt{109}}{10}
$