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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-21x^2+35x-(2x-7)+5=0

We get rid of parentheses

-21x^2+35x-2x+7+5=0

We add all the numbers together, and all the variables

-21x^2+33x+12=0

a = -21; b = 33; c = +12;
Δ = b2-4ac
Δ = 332-4·(-21)·12
Δ = 2097
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:

$\sqrt{\Delta}=\sqrt{2097}=\sqrt{9*233}=\sqrt{9}*\sqrt{233}=3\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{233}}{2*-21}=\frac{-33-3\sqrt{233}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{233}}{2*-21}=\frac{-33+3\sqrt{233}}{-42}
$