5x(-2x+7)+3=-10x+38

Solution for 5x(-2x+7)+3=-10x+38 equation:

5x(-2x+7)+3=-10x+38

We move all terms to the left:

5x(-2x+7)+3-(-10x+38)=0

We multiply parentheses

-10x^2+35x-(-10x+38)+3=0

We get rid of parentheses

-10x^2+35x+10x-38+3=0

We add all the numbers together, and all the variables

-10x^2+45x-35=0

a = -10; b = 45; c = -35;
Δ = b2-4ac
Δ = 452-4·(-10)·(-35)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-25}{2*-10}=\frac{-70}{-20}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+25}{2*-10}=\frac{-20}{-20}
=1
$