4x(x+5)=10x+3

Solution for 4x(x+5)=10x+3 equation:

4x(x+5)=10x+3

We move all terms to the left:

4x(x+5)-(10x+3)=0

We multiply parentheses

4x^2+20x-(10x+3)=0

We get rid of parentheses

4x^2+20x-10x-3=0

We add all the numbers together, and all the variables

4x^2+10x-3=0

a = 4; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·4·(-3)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{37}}{2*4}=\frac{-10-2\sqrt{37}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{37}}{2*4}=\frac{-10+2\sqrt{37}}{8}
$