10x-3x(x-5)=7x+3

Solution for 10x-3x(x-5)=7x+3 equation:

10x-3x(x-5)=7x+3

We move all terms to the left:

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

We multiply parentheses

-3x^2+10x+15x-(7x+3)=0

We get rid of parentheses

-3x^2+10x+15x-7x-3=0

We add all the numbers together, and all the variables

-3x^2+18x-3=0

a = -3; b = 18; c = -3;
Δ = b2-4ac
Δ = 182-4·(-3)·(-3)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12\sqrt{2}}{2*-3}=\frac{-18-12\sqrt{2}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12\sqrt{2}}{2*-3}=\frac{-18+12\sqrt{2}}{-6}
$