5x^2+5x+3=12

Solution for 5x^2+5x+3=12 equation:

5x^2+5x+3=12

We move all terms to the left:

5x^2+5x+3-(12)=0

We add all the numbers together, and all the variables

5x^2+5x-9=0

a = 5; b = 5; c = -9;
Δ = b2-4ac
Δ = 52-4·5·(-9)
Δ = 205
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{205}}{2*5}=\frac{-5-\sqrt{205}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{205}}{2*5}=\frac{-5+\sqrt{205}}{10}
$