11x+3=5(4x^2-3)

Solution for 11x+3=5(4x^2-3) equation:

11x+3=5(4x^2-3)

We move all terms to the left:

11x+3-(5(4x^2-3))=0


We calculate terms in parentheses: -(5(4x^2-3)), so:

5(4x^2-3)

We multiply parentheses

20x^2-15

Back to the equation:

-(20x^2-15)


We get rid of parentheses

-20x^2+11x+15+3=0

We add all the numbers together, and all the variables

-20x^2+11x+18=0

a = -20; b = 11; c = +18;
Δ = b2-4ac
Δ = 112-4·(-20)·18
Δ = 1561
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{-(11)-\sqrt{1561}}{2*-20}=\frac{-11-\sqrt{1561}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{1561}}{2*-20}=\frac{-11+\sqrt{1561}}{-40}
$