4x^2=5-3x

Solution for 4x^2=5-3x equation:

4x^2=5-3x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

4x^2+3x-5=0

a = 4; b = 3; c = -5;
Δ = b2-4ac
Δ = 32-4·4·(-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{-(3)-\sqrt{89}}{2*4}=\frac{-3-\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{89}}{2*4}=\frac{-3+\sqrt{89}}{8}
$