5x(x+2)-3=3x-8x+7

Solution for 5x(x+2)-3=3x-8x+7 equation:

5x(x+2)-3=3x-8x+7

We move all terms to the left:

5x(x+2)-3-(3x-8x+7)=0

We add all the numbers together, and all the variables

5x(x+2)-(-5x+7)-3=0

We multiply parentheses

5x^2+10x-(-5x+7)-3=0

We get rid of parentheses

5x^2+10x+5x-7-3=0

We add all the numbers together, and all the variables

5x^2+15x-10=0

a = 5; b = 15; c = -10;
Δ = b2-4ac
Δ = 152-4·5·(-10)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{17}}{2*5}=\frac{-15-5\sqrt{17}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{17}}{2*5}=\frac{-15+5\sqrt{17}}{10}
$