4x(x+3)=10

Solution for 4x(x+3)=10 equation:

4x(x+3)=10

We move all terms to the left:

4x(x+3)-(10)=0

We multiply parentheses

4x^2+12x-10=0

a = 4; b = 12; c = -10;
Δ = b2-4ac
Δ = 122-4·4·(-10)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{19}}{2*4}=\frac{-12-4\sqrt{19}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{19}}{2*4}=\frac{-12+4\sqrt{19}}{8}
$